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To my knowledge, nobody has been sentenced to slavery in a long, long time. On the other hand, the US has managed to lock up 2% of its population and force them to labor in circumstances and rates that would be illegal for free citizens in order to guarantee the profit of private corporations. That this system of arbitrary law enforcement[0] disproportionately hits the same sub-group that used to be literally enslaved really should send your eyebrows through the ceiling when the defense is that it's not literally slavery.
Of course, US prisoners are not chattel slaves; they're not literally property, and neither are their children. On the other hand the rate of recidivism in the US, and the strong correlation of outcomes between parent to child makes this kind of a cruel joke. If your father having been in prison makes you overwhelmingly likely to end up in prison yourself for similar reasons, it's hard to put on a straight face and pretend that nothing is wrong.
I'd argue that this structure represents something akin to stochastic terrorism, but for forced labor. Stochastic terrorism is a case where someone or some group attempts to radicalize and encourage terrorism from afar. Done correctly it produces a statistical probability of terror attacks without anyone (even the group) being able to predict the exact time and place. These types of systems are very hard to disrupt, which is why groups like ISIS leaned on them in order to attack the west, which had gotten very good at stopping more organized attacks.
Similarly, I'd argue that the US system represents a type of stochastic slavery. It's impossible to precisely predict who will or will not end up in the system providing free labor (unlike chattel slavery, where it's very easy to predict), but one can easily calculate the aggregate chance of someone ending up in prison. It's not literally slavery, but with the recidivism rate so high it ends up functioning like it for most people caught up in it. Oh, and it's run for a profit too, which is deeply concerning.
0 - Drug laws remain key to why America has so many people locked up, and drug law enforcement is incredibly arbitrary, both in terms of which drugs get which sentences, and who gets the hammer dropped on them when they get caught.