FDIC has exactly 0 to do with this.
Competent risk management so that doesn't (generally) happen is a core competency for a bank, and if regulators think you're doing it wrong they will come down on the bank's leadership like a ton of bricks.
If anybody reading this comment would like to learn more from people who understand the area far better than I do, I would recommend patio11's 'Bits About Money' and Matt Levine's 'Money Stuff.'