The criminal case against Lay ends with it undecided from a legal standpoint. Nobody is going to sentence his body to a jail cell, nor are they going to decide whether his appeals had any merit.
It just stops. His conviction isn't reversed or halted. That happened.
The only legal effect is that it won't be possible to use the criminal conviction in any civil proceeding to seize his remaining assets. But that's not a huge obstacle. It's no different than if he had pleaded no contest at the criminal trial.