Well that's a secret ! If I told you your bones might end up in a jail cell somewhere. :)
Where criminals were hanged in the UK (a practice we abandoned 42 years ago) they were always interred in the confines of the prison in which they were hanged. Nowadays, I think it is up to the "next of kin" - if there are no relatives, I think they get a paupers grave in the nearest cemetary. Curiously, since there has to be permission for a cremation, if there is no-one to give such permission, they just get buried.
This answer on Quora seems to make sense:
When an inmate dies, one of two or three things can occur to the body. The family/next of kin can take it and accept the responsibility of disposing of it. Whether burying or cremation is chosen, they can do whatever they please.
The prisoner may have previously filled out the proper forms to donate their body to science. If that's the case, it is kept on ice until the proper authorities arrive and take the body off their hands.
Lastly, if nobody claims the body or has been assigned to take custody of it, then the state either cremates or buries it in a cemetery nearby, which has been created for such a situation.
The actual steps involved in the process may vary---for example, When Charles Manson died, a number of different people sought to claim the body. The courts awarded custody of the body to the grandson.
(As for immediate disposition of Manson's body, since the prison in which Manson died did not have the proper cold storage facility, the county coroner took interim custody of the body.)
They are dead. What difference would anything make?