So if you have $300k in Bank A, and $180k in Bank B, and then suddenly both Bank A and Bank B fail, the US Federal Government promises you'll get $250k from Bank A and $180k from Bank B, and pretty quickly - but the remaining $50k from Bank A depends on what happens when they try to wind up Bank A, if it's a complete wreck you may see nothing or almost nothing back or it may take years to get 10ยข on the dollar for the remaining amount.
In some cases you may be able to create multiple ownership categories that help you, and I guess if you really had $16M you might do stuff like set up a multi-beneficiary trust fund that can have $1M in it with four beneficiaries for an additional $250k per person FDIC insured.
The reason is that since the government owns this bank, and the government issues the money, if the bank fails the government fails too and the money is now worthless anyway.
For that to fail, the whole world economy would need to fail as well, and at that point, no money on any currency is worth anything.
That way if something goes awry, I still have the rest.
For regular bank account, there are no other underlying assets, it is just the sum bank owes to the account holder. If the bank becames insolvent, outside of insurance limits, these are just claims against the bank.
But it's still in a bank account, so if the bank goes under you're screwed. See my other comment in this thread though...
The Securities Investor Protection Corporation (SIPC) was created to protect against the loss of customer assets at brokerage firms. SIPC offers protection of up to $500,000, including a $250,000 limit for cash, if a brokerage firm fails, and covers most types of securities, such as stocks, bonds, and mutual funds. [0]
[0] https://www.schwab.com/public/file/P-3042070/Asset_Protectio...