You're referencing those who can kill screen at will on a single man running boards, but I don't believe it matters that it's the last life.
The same people could do it on their first life too if they really wanted. Given this logic I would find it hard to believe there'd be an exception to the rules if a player were to kill off their first three lives and run boards on their 4th for the remainder of the game.
If the first man bounty were taken, I have a feeling those same people I'm referencing have a much bigger fish to fry than going after the bounty you're referring to.