Answer:
Yes, it does. It is an arm of the federal government, and not truly "insurance". Instead, it is more in the nature of a bail-out fund that the government operates to make whole, to a statutory limit, depositors in failed banks.
When the FDIC determines that a bank is failing, it may attempt to salvage it by appointing itself as a receiver to run it and get it back on its feet. If that is not possible, the bank will be liquidated.