*Warning, rather long post here*
The Escape from the Underdark setting assumes that most characters escaped from slavery, but of course not all since some are lost adventurers who were never slaves or are the children/grand-children of escaped slaves who were born free in Sanctuary, which adds a new dimension to role-playing a character. Some players will want to take time to consider how slavery affected their character, and what impact the experience left upon them. None of this is "canon" or even technically in line with what the DMs may have in mind for how some of the slave keeping races treat people, but I thought starting a dialogue will be helpful at least--and many of the ideas are just my best interpretation of how things would work. Some of the information on slavery is drawn from real world sources, especially the book Debating Slavery by Mark M. Smith, and I'd also recommend Dan Brown's Slavery in the Ancient World.
Kinds of Slavery
Chattel Slavery (Drow, Goblinoids, Stone Giants, Aboleth, Yuan-ti, Lizardfolk)
There is more than one kind of slavery, most people are familiar with the chattel slavery depicted in the American South-I won't go deeply into a debate about whether it was what most people are familiar with or not, but suffice to say the "image" most people think about with poor living conditions, humans treated far worse than any animal, frequent whippings, poor nutrition is what "chattel slavery" looks like in a typical fantasy setting. Lizardfolk in Slaal'teesh make engage in Chattel slavery, but for them the slaves are not kept as much for 'tasks' as to perform medical expiraments upon. Chattel slave work is often done by "chain gangs".
Patron Slavery (Duergar, Fire Giants, Kuo-toa, Dragons, Necromancers/Undead {rarely keep any living slaves, relying on undead minions, but occasionally one gets whimsical ideas})
A second form of slavery is what most people tend to think about when they think of slavery in ancient Rome or Greece. A lack of any basic freedom, but slaves are generally treated like favored servants in the households--perhaps treated like good work animals or favored pets depending on whether they're in the home or out in the fields/mines. Slaves are still punished, but the masters typically do try to treat their property well and ensure the slaves are healthy and strong not necessarily because the master cares about the slaves. Slaves in some patron systems may eventually even be freed. Patron slave work is often done on a "task system", with certain jobs assigned to individual slaves. Occasionally, drow will employ the Patron system for household slaves or even an attractive "pet" they keep for ascetic reasons.
Mental Slavery (Beholders, Illithid, Aboleth, Ancient Dragons)
A form of slavery that only exists in fantasy settings, mental slavery takes the form of slaves compelled into bondage by entirely magical means. They have no free will, they're not treated as "less than animals" as in the Chattel system but are considered nothing more than tools. As tools, they're well cared for, used for specific and specialized tasks (because after all you can hammer with a hammer, but a hammer isn't smart enough to drill a hole i.e. you can charm a slave to mine, but if you want the slave to guard a gate that takes a reapplication of the charm/dominate process and isn't likely worth the effort).
Kinds of Masters
Beings keep slaves for a number of reasons, but the most common reasons are related to either economics (the drive for more money/power/slaves or social with slaves viewed as 'savages needing civilization' generally meaning slaves aren't from the dominant culture and aren't considered capable of belonging to it.) When slaves are kept for economic reasons, slave conditions tend to be better often more "Patron" like, while slaves kept for "social" reasons may find their treatment for "Chattel" like although a strong exception here is when the master culture thinks the slave can ultimately learn and join the culture of the master--in which case the slavery takes on the "Patron" connotations. Illithids occasionally keep slaves around for bizarre "organic art" constructs. Slaal'teesh's lizardfolk keep them purely for medical expiraments.
Illithids and Beholders tend to follow Mental Slavery patterns.
Goblinoids and Drow typically keep Chattel Slaves.
Duergar may vacillate between Chattel and Patronage systems, depending on their needs. They don't care much about slaves as living beings but some fall into the Patron system because they feel treating their slaves better will yield them larger profits, others use the Chattel system hoping that working slaves to exhaustion will yield larger profits--at the core here the availability of getting new slaves often drives conditions.
Slave Life
Slave reality has a great impact on slave culture. Slaves are typically forbidden to read, reading allows slave's access to education and knowledge which can cause them to become disruptive. Even slaves that can read are not likely to teach others in a Mental or Chattel system; those that try in the Chattel system are likely killed. Slaves kept in a Patron system may be allowed to read; or even obtain some education to make them either more valuable as slaves (slave tutors for example) or in the hopes the slave can learn to better mimic the master's society.
Religion is generally forbidden by all masters. Religion gives slaves hope, a feeling of security and opportunity, and the sense a larger power "cares" about them or will grant them blessings i.e. tools to escape bondage. In chattel systems, the religious are generally killed. In Mental systems, the religious typically brainwashed to forget their beliefs. The exception is the Patron system, which may encourage slaves to adopt the religion of the master society, although some masters may believe slaves aren't "fit" for worshipping or approaching the divine.
Language is a valuable tool that allows slaves to communicate. Often slaves will speak languages that the masters do not know, and can use this to plan rebellions, resistance, and more. As a rule of thumb, all masters forbid speaking languages other than those they regularly use themselves and severely punish slaves who resist in this matter.
Magic is important in fantasy settings. However, spell casters make poor slaves. If they are divine spell casters, they bring all the danger of religion and regular wizards. Arcane casters are an incredible danger, it is impossible for a master to know the true strength of an arcane caster, and most are too physically weak to be useful slaves. Wizards and sorcerers may be kept on as scribes, retained for their scholarly knowledge. If they are kept, any threat they can be is neutralized: they may be blinded so they can't see to target spells, crippled to prevent them from making the necessary gestures to cast, or their tongues cut out. If the slave is too valuable to maim in this manner, the master either is too strongly attached to them: or they are kept separated from other slaves often locked away somewhere that their owners have easy access to them from their libraries or laboratories. Almost any wise master kills a divine spell casting slave before they can incite resistance or rebellion, even in the Patron system it's just too dangerous for the slaves to think any power greater than their master may be capable of affecting their lives.
Daily Life for chattel slaves generally involves hard labor all day, generally with one meal early in the morning and a smaller one late in the evenings, nutrition is based most often on the ease with which replacement slaves can be procured. There is little to no free time, slaves generally associate only when working in chain labor with distracted or bored supervisors. In Patron systems, slaves tend to eat meals after the master has his meal and often will eat whatever scraps or left-overs remain, duergar prefer to feed their strongest animals first so males often eat before females. Free time is often higher due to task-systems, in which a slave is given a certain task or tasks to perform in a day, once those tasks are done they often may spend the remainder of their time doing their own business; generally this involves growing a little food, or using scraps of cloth to make clothing, bedding. In Mental systems, daily life simply does not exist although slaves kept far enough from the master, out of sight can often mean out of mind--and the master may forget to renew the domination of the slave; frequently this is the only way slaves get a chance to escape from such bondage.
Slave life can often change during warfare. Slaves are rarely used in warfare since there is a danger in arming large numbers of slaves, who may join your enemies. Occasionally though, a master grows desperate or wishes a distraction, or even promises freedom to slaves who fight for them--this is mostly only possible in Patron systems. In Mental systems, slaves are often forced into battle, proving an exception to the rule. In Chattel systems, there is occasionally the use of slaves as spell fodder, large numbers sent unarmed or poorly equipped toward enemy positions to draw off fireballs and similarly destructive war spells away from the main forces.
Being crippled as a slave isn't necessarily the end of bondage even in the chattel system. Indeed, some slaves are crippled purposefully by their masters. Skilled artisans may have legs crippled to prevent them from running away, drow occasionally cripple females who try to commit suicide or murder their own children rather than allow them to be born into bondage, miners may have legs removed to prevent them fleeing into mine shafts.
Slaves that do manage to form society learn quickly to keep it hidden. Gang labor frequently develops with a clear leader who makes immediate decisions but allows the group to share with the process, this prevents strong leadership and encourages a more democratic outlook not necessarily by desire but frequently by necessity as in chattel systems strong leaders are singled out and often killed. In Patron systems, leaders are often favored slaves.
Slaves often do tell many stories, especially they're fond of stories about escaped slaves-but of course master's punish those who tell these stories harshly, so the slaves often learn to disguise the stories using jargon and metaphors to carry their messages i.e. in drow slave societies many stories about Jack Spider, a wily arachnid that frequently played tricks and pranks on foolish monsters in the Underdark are common--the drow priestesses often looked with patronizing amusement on these stories, frequently ignoring their underlying theme when viewed by slave races of a weak insect outsmarting the strong and powerful.
Resistance is common in the Chattel and Patron systems both. Workers will often work as slowly as possibly, fulfilling quotas required and no more, many slaves are punished for sabotaging equipment although they always claim it "broke" on its own, other slaves feign stupidity and claim to not understand how to perform tasks; even after days of doing it although this behavior is often harshly punished.
Family life is generally impossible in the Chattel system. Women and men are exposed to one another to breed only, and then the pregnant female is often removed immediately from the male to prevent any bonds from forming between them, the child when it is born is treated similarly and often given to a wet nurse. Slaves with families tend to be more resistant to their situation, so Chattel slavery does all it can to prevent family from developing. In Patron systems, a master may actually encourage a family to develop believing it will help civilize the 'savages' and the master quickly learns it's easier to punish the slave's family for transgressions than the slave.
Effects of Slavery
The effects of slavery on the victim are great and long lasting. All slavery tends to dehumanize the victim, in Chattel systems the victim is treated like an animal and may very well become more feral; use to only the barest necessities being met. The Patron system is more sinister in some ways; the victim may be treated with more dignity than in a Chattel system, but quickly develops a sense of less worth than the master and members of the ruling class. This breeds an innate child-like subordination (often this childlike state is encouraged by the master's themselves who treat slaves as either stupid, or merely wayward children who can't possibly operate at the same level as their 'adult' masters), this is coupled with an inability to make strong eye contact and hunched body language, and there is an encouragement of weak will in slaves in all systems, those with stronger wills are frequently the most severely punished. In Mental systems the victim is often stripped entirely of personality, if escape happens the victim may not even remember what their original life was like, or even who they were. The first memory of many slaves who escape the illithid are of suddenly being somewhere unfamiliar, further away from their masters than they've ever gone before, somewhere frightening and where they're left feeling alone and confused.
Life expectency varies but in Chattel systems life expectancy of 17% the normal is common with few living past their prime as an old slave is generally not as worthwhile. Patron systems tend to be less unforgiving but an expectancy of 25% the norm is still the average although slaves may live longer if they are favored. In Mental systems, slaves are generally kept alive into their prime, 50% max life expectancy before being disposed of--illithids generally devour their slave's minds and feed the remaining husk to the other slaves, while beholders enjoy killing their slaves in entertaining and unique manners.
Punishment frequently leaves more than just scars from lashings, slaves may have body hair plucked out by drow who find it disgusting, duergar prefer to brand their slaves on the back or chest, and illithids enjoy experimenting with bodies, frequently implanting strange organs or skin grafts which they come to view as 'art'. Slaves may have limbs removed if they are not necessary to a job and encourage the slave not to flee, many slaves have tongues removed. Drow females frequently castrate male slaves for amusement.
Rewards for Slave exist in all systems except of course Mental. Rewards often take one of four forms, mobility which is essentially a transfer from harsher more degrading work to easier (in context) obligations, better shelter, the right to breed, or better food. Occasionally in the Patron system, slaves are even allowed to make their own crafts and possessions with left over material when their tasks for the day are done; nothing too good or the master will simply claim it for himself.
Escape*more planned for here*
Escaping is a defining moment for any slave. Regaining freedom is frightening for many slaves, unuse to making choices, dehumanized by their living conditions, degraded and taught to rely on strong masters for food, shelter, and alone in a hostile and unfamiliar setting such as the Underdark. Freedom may even bring about depression and total alienation, some slaves may seek to end their own lives, or even attempt to return to bondage overwhelmed at the options freedom brings. Frequently, slaves are leaving behind something--in the Chattel systems children who were taken from them upon birth or conception even, lovers they gained as rewards from masters, in Patron systems they may even be leaving the 'comfort' the master provided, a family they were allowed to have, or possessions they were allowed to accrue. Escapes from Mental systems are absolutely bewildered by their sudden free will, and nihilistic self destructive tendencies tend to be greater with these freedmen.