The bank (every single bank) pays the FDIC a fee on every insured bank account. The FDIC puts all that money into a bucket and pays out from it whenever a bank

The bank (every single bank) pays the FDIC a fee on every insured bank account. The FDIC puts all that money into a bucket and pays out from it whenever a bank fails. They also have a line of credit with the Federal Reserve that they can draw on if the bucket isn't large enough. So the FDIC pays out everybody up to $250k, closes the bank, liquidates the assets, and then pays out the balances above $250k until they run out of money.