E:D Wiki
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It was shaming to do something that put people in a bad state. The poorhouses still happened, but sensibly, people were supposed to look after each other.
Yes, I am aware that several senators are not living up to that standard, but as they have been placed above the law I would not consider them ordinary Imperial citizens.
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Imperial Citizens (aka Imperials or Imps) like to project their wealth. They prefer opulence, style and quality with no expense spared. This is visible in their cities, ships by Gutamaya and clothing.
In a way the slaves you own are just another way to project said wealth. You dress them well as yet another way of saying "Look, I haz shiniez!"
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In many Imperial families there is little direct interaction between the parents and their children other than at ceremonial events where they are required to perform roles. Children are attended by Imperial Slaves from a young age. Children within the privileged upper echelons of the Empire are indoctrinated into Imperial style, intonation, dress and decorum as befitted their parent's socioeconomic status in society.
This means that there is A LOT to do inside the Empire for Imperial slaves.
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The Empire relies less on mechanical technology such as robotics and artificial intelligence, and instead uses Imperial Slaves and clones to do the work which machines usually perform in other parts of the universe.
And if I remember correctly "robotics" tended to be illegal goods in Imperial systems in "Frontier: Elite II" and "Frontier: First Encounters". I assume that changed when Aisling began her anti-slavery movement.
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Source
And to answer that other question that A C Ender asked how long this endebted servitude lasts:
While I've not found anything solid yet I'll stick with an opinion I posted earlier for now: It depends on how large your debts were and what services you were willing and/or capable to offer.