Because of the FDIC the next bank run will be different. It won't be a mad dash to get dollars, we can get those for sure. It'll be a dash to get value for our dollars. There is and can be no guarantee on that. I suspect people who have no more room for cans of beans and toilet paper will try to get some of their wealth through the crisis in gold and bitcoin.
The FDIC has almost no money. The banks that fail every Friday like clockwork have depleted the insurance fund completely. Sheila Bair is operating off of a 500 billion line of credit with Treasury, which will not be nearly enough to prevent a bank run should a TBTF go down. Increasing that line of credit literally requires an act of congress, meaning it wouldn't happen in time to do any good. Besides, Treasury is Broke too.
Bank runs are always, always deflationary, but the big financial crisis may not be a bank run. It depends on how much liquidity the FED provides. Too much and the ship alters course from Japan to Zimbabwe.