That’s an absurd assertion. No, to a customer, a bank run is rapidly dealt with via the FDIC; we just had a great example of this with SVB. Madoff’s victims were not so lucky.
The FDIC made that happen. SVB became illiquid which triggered FDIC intervention. The bank was shut down by the FDIC and the assets were sold off to First Citizens bank. Executed without a hitch and no customer assets lost. The only ones who lost money were investors in the bank.
The FDIC would never make someone acquire a Ponzi scheme. Someone could in theory do it, but why would they? It's just throwing away money.
