As for the collateralization of the DAI, to what extent is this sufficient in case you have a bank run?

It was very sad and traumatizing to see what happened to LUNA in recent times. So I started to wonder how other stablecoins will work if they are subjected to a stress test. I was curious about DAI, I know it is supercolatized. However, I would like to know about the risks that the protocol can offer if there is a possible bank run. What would likely happen within the protocol in this situation?