No. The money would come from the federal deposit insurance program, which is funded by the banks, not the government. The money would also be recovered over time, when the bank’s loans become due and other assets are liquidated.
In general the money would come long before the FDIC get involved, because the role of the Fed (and other country equivalents) is ensuring that commercial banks can always borrow enough money to meet short term withdrawal requests if their loans aren't defaulting. Lending at n+x% because it can always borrow at currency at n% is a modern bank's business model.
Needless to say this is quite different from having a business model where you don't have any right to borrow money and claim to be backing it 1:1 with actual dollars, but it turns out that the bulk of the not-necessarily matching amount of actual dollars you have is lent out to some other shady operation...