I think there is an edge case where both people die at the same time, but one is about to make a move and drops the piece as they die, and it lands on the board. Is that move valid? Or not as they are already dead when it lands?
Typically there will be a clock involved, your move is completed when you push the button on the clock. Merely dropping a piece on the board doesn't complete your move.
However, I can see a situation where the player dies and falls on the clock, pushing his button.