But in the case of the bank being hacked, I could imagine it affecting enough accounts that the bank cannot cover it. Would that count as the bank failing (or perhaps a run on the bank?), and so then be covered by FDIC insurance?

Finally, suppose the hack is a case of financial terrorism. Say, a state sponsored group is trying to undermine confidence in the banking system and so wants to be as disruptive as possible. Instead of just getting in and stealing some money, they have been in for months and have been sabotaging things. They mucked with the backup procedure to make it so the backups are corrupt, and the bank unwisely did not do actual restore tests on samples to check things. Finally, the hackers set everyone's account balance to zero (or more fun, delete everyone's account).

So now my bank has no idea how much money I'm supposed to have (or even if I'm a customer). They fail and FDIC steps in. Do the banks have to periodically give the FDIC or other regulators lists of accounts and balances, so that FDIC would be able to at least figure out things up to the last month, say, or would the FDIC also have no idea who gets what?