I honestly don't know (what happens to the most egregious sinners of all time -- Hitler, Stalin).
Let me guess -- out of sight and out of mind. Probably in contrast to Schadenfreude that some Christians suggest, a ringside seat to watch torments inflicted upon such types as Pol Pot and Saddam Hussein.
In the summer of 1980 I was in Hell -- Dallas that year. On a day on which that the temperature reached 113F I made the flippant remark to a Jewish co-worker that I had just seen Hideki Tojo. Or was it Benito Mussolini? I was saving Stalin for 114F, but I had gone through a series of Wild West outlaws, gangsters, dictators, and war criminals. The co-worker didn't get it, and it wasn't for a lack of intelligence or ability to appreciate grim humor. So there is no Hell in Judaism? If any people has villains to condemn, it is the Jews.
I once engaged a Nazi sympathizer (a piece of work -- a Holocaust denier and a horrible hypocrite on European-Arab relations... the sort who loved Palestinians as fighters of his nemesis Israel but didn't want them living in Europe or the Americas) on a now-defunct Forum and eventually got him into a discussion of Dante's
Inferno in which I challenged him to contemplate what eternity would be like for people even worse than the well-characterized sinners of Dante's time. Dante Aligheri could have never contemplated Nazis, Stalinists, the Khmer Rouge, and Ba'athists. Maybe one could imagine Karl Marx (at least to conservatives of the 20th Century) being consigned to the peculiar torment that Dante allotted to Mohammed for "tearing the world apart with his heresy". I could imagine Nazi hanging judge Roland Freisler dangling forever on piano wire from a meat hook as was the sentence that he imposed upon those that he convicted of the July 20 plot. But such takes no imagination.
But ignore the sensory insult and deprivation... I asked him whether he wanted his soul to be around those souls who betrayed, lynched, tortured, robbed, beat, and murdered people. Sulfurous smells, hunger, thirst, and general ugliness are less ominous to me than being around the grossly-unjust. Maybe I would get some grim satisfaction out of seeing Josef Goebbels getting his lies pushed back into his mouth as lye, with predictable effects. But I wouldn't want to see such for long. "Out of sight and out of mind" is best for all.
Performances of operatic collaborations between Shakespeare and Mozart would be a fitting eternal reward for the righteous.