Well, that's not quite true. There is always a small risk of losing some (or even all) of your money, particularly if you have a large amount in your account. Obviously that risk is very, very low for smaller amounts of money.
Assuming your account is under the FDIC limit, how could you lose money on an insured account? Suppose there's a massive bank run and the Fed has to print oodles of cash to repay depositors. This leads to runaway inflation that occurs over a very short period. If you could have otherwise exchanged your cash on hand for a different currency, sure you would have lost money.
Compared with the actual risks of being unbanked, this is a hallucinatory concern.