It would very much depend on the nature of his death.

If he was assassinated, Russia would go full gloves off and completely destroy Ukraine and or Zelenskyy government.

If he died naturally (and it was believed legit), public support would determine the next steps. Unfortunately, must Russians generally support their governments war so things would probably stay on a similar trajectory.

The USSR collapsed for a great variety of reasons and I don’t think it’s really comparable in this case. Russias current government is neither communist nor a group of significantly distinct peoples (the Caucus region excluded). Russia would in almost all probability not collapse, they still have the resources the world needs and they have allies outside the west that will see them through.