Remember that scene at the beginning of It’s a Wonderful Life, where people are all desperately trying to get into the bank because if it fails before they get in, they lose their money? That’s what the FDIC prevents.
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That’s a little hard to parse, but if you’re asking “What guarantees the FDIC has the money to pay back Americans who lose their savings because of a bank collapse?”: The FDIC does. From https://www.fdic.gov/about/what-we-do:
FDIC insurance is a selling point for many retail banking products (like checking and savings accounts), so those institutions pay for the insurance so people will have confidence to bank there. More importantly, they buy it because it’s required by law currently.
If the FDIC were abolished, the void would be filled by unregulated entities that would charge higher premiums and cover less, and there would probably be kickbacks involved - while the government watches with its popcorn - to disincentivise real free market competition.
That’s if there were any kind of deposit insurance at all, I mean. The idea might be to encourage the American people to put their savings into a form they can retain control over - like precious metals, land, or digital currencies.
There’s also an implicit guarantee that the federal government would step in an make deposits good if there were a bank failure large enough to wipe out the FDIC