From the little ball board...

[Dholloway1962]

Originally Posted by CecilOne

why is the ball dead? Is it just because the inning is over?
What if the defense plays on another runner, gets that out, and then the original presumed third out is overturned?

Ball is dead because the inning is over. They can't make a play on another runner. They can make an appeal for the 4th out but only a dead ball appeal. You can't tag out another runner for a 4th out/insurance out.

Rule 10 does allow for an umpire to rectify a situation were a runner was placed in jeopardy. Once that umpire called the 3rd out he has placed all other runners, and defense for that matter, in jeopardy so you won't honor that "4th out" play on another runner, just like you won't allow a runner to score after the 3rd out.