Person A can only sell the number of shares they've borrowed. If Person A borrows a share from Person C, they can sell that one share only. To sell more without borrowing additional shares would be naked shorting, which is prohibited.
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.
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.