Passive index funds will have shares held in custody by a...

Passive index funds will have shares held in custody by a custodian. Aiming to better match the index post management fees, the index manager can reduce fees by loaning stock out.
Since the index fund doesn't care if the price goes up or down the manager is happy to lend our the stock and receive a fee for that. As long as the stock is in the index, they can lend out those shares indefinitely.

An example of what can cause a short position having to be close is as follows:
Some active managers may hold shares in custody accounts that allow the custodian to lend shares out for which they'll also receive a fee. On occasion the active manager could change their mind and move those shares into a different custody account from which share lending is restricted.
In that case, the broker/custodian lending out the stock would have to find another willing lender of the same stock which it could offer to the borrower. Otherwise the stock will be called back from the borrower to satisfy the change of account status by the active manager .