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It's actually really simple. The parties short seller sold to can lend their shares out again.

Say I own the only share in Acme Corp. A borrows it and sells it to B. B then lent it to C who then sold it to D. Now you have both A and C with short position, despite only one outstanding share.

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Sure, but they can't both cover it, as D can only sell it back to one of them to return to you. It only works if everyone essentially does the trade in reverse, which requires (illegal) coordination.

The key insight is the order of reversal doesn't matter, and that any securities trade/position is eventually reversed (its the only action available). Hence having synthetic positions outstanding via rehypothecation doesnt actually matter as they are fungible with normal float.

is eventually reversed (its the only action available)

But this assumes normal market operation, which a short squeeze is not. Suppose in the example above A buys the share from D and sells back to the original issuer, who then refuses to lend it out again. C can't pay back B and presumably goes bankrupt.

It only makes sense if people are required to lend securities to anyone who wants to borrow them.

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