So in this example person A could keep selling the same share over and over again? How would the multiple “owners” realize their gains if they all decided to sell on the same day?
You might be asking instead about the following scenario, though, where a single share is borrowed and sold short multiple times:
Person A borrows from Person C and sells to Person B
Person D borrows from Person B and sells it to Person E
Well, the covering of the shorts doesn't have to happen in an atomic transaction; there are thousands to millions of trades of a single ticker every day. Just as a single share can create a chain of multiple shorts (borrows and sales), a single share can cover multiple shorts too through a chain of trades.