If you're the executor and have POA and can prove it the insurance company will do whatever you want - regardless of whether the man is dead or not because you have POA !!! Personally on a $10k car, I'd drop all insurance unless it looks like the roof IS ready to cave in. Dispose of the car a.s.a.p.. - there is no reason to keep it sitting around. When it comes to estates you want to cancel any utilities, etc. that are non-essential and liquidate assets as quickly as possible. Its a lot easier to divvy up the estate when everything is cash - trying to divvy up assets only results in arguments.

When my uncle died we had his car sold within a week - my aunt doesn't drive.
When my dad died there was more money owing on the car than the car was worth due to a lousy trade-in deal they had pulled on him. The car was the only thing in his "estate", everything else was already in my mother's name, we walked into the Ford dealership and tossed them the keys and ownership (the loan was with Ford Motor Credit).