What's the difference between the former slave being awarded the judgment at the time and their heirs being awarded the judgment now? Legally speaking, there is nothing unique about that situation.
No. Wrongful death claims are pursued by heirs or estate administrators. That can include spouses, parents, children, grand children, and other heirs depending upon the state. In addition to wrongful death, we also have the concept of survival rights of action. That is that causes of action you have don't die with you but can be pursued by the inheritors of your estate. So, if you're injured a car wreck and then die of an unrelated event, your estate/heirs can still pursue legal action related to the car wreck.
Further, you're mixing up criminal and civil liability in a weird way. While civil liability can be predicated a criminal act, a criminal act isn't necessary. And, ultimately, reparations wouldn't be handled through our civil justice system anyway, but rather through tax policy, so I'm not sure why we're exploring this weird and irrelevant rabbit hole.
War reparations have been a thing for a very long time. I also don't find the argument that bad shit wasn't correct before so bad shit shouldn't be corrected now as terribly compelling.