More people are killed by car crashes than firearms. That's an undisputable fact. Banning all forms of motorized transportation and going back to horses and wagons would reduce the amount of deaths far more than banning all privately owned firearms. If you want to pass laws to promote safety and prevent deaths, then look at where you can find the most gains.
Banning cars is not politically correct though, and banning firearms is an easier sale to the general public.
When a person dies, their possession become part of their estate, which a living person is appointed as an executor or an administrator over. The estate functions with the same rights and responsibilities as a living individual until all assests have been distributed and the estate is dissolved. I've had to handle them before, and I am handling one currently.
So, yes, the Fourth Amendment, should apply to the living administrator/executor of the estate who is legally responsible for the assest that happens to be a firearm.