This question does a nice job of answering what it takes for short position to exist in the first place, how that can result in "owning" >100% of a company and what happens when shorters try to cover their short position with limited liquidity (i.e. how a short squeeze develops).
What I'm wondering is the different question (which I tried to ask here, which was closed as a dupe of the first): what happens if short sellers are somehow required to cover their position (i.e. required to buy at any price) but where there are NO shares being offered regardless of what price is offered? Every single last share is held by someone either unwilling or unable to sell it.
The details of how to construct such situation are not very relevant so I'll try not go into them.
It's possible the answer to my question is, "it's never happened, the law and regulators never considered it and until/unless it does happen, there is no way of knowing what would be done." If that's the case, then "oh well, maybe it would be fun to write a fiction book around that". But I'm kind hoping that someone knows something more definitive.