In such a scenario, people will turn to gold.
Bitcoin's adoption is not that widespread for it to be considered as a safe asset for common people.
Banks have tided over bigger crises than this.
Banks will not "tide over" a 19 TRILLION dollar hole of debt, when the interest payments come calling.
As for gold, there are logistics to it that are necessary to attend to, like making sure you aren't being sold gold-cladded garbage - like some in NYC found out when buying bars. Even coins aren't immune to potential counterfeit attempts. Unless you want to become an expert at assaying, you are taking a risk every time you trust a gold seller with your money. (Much like any other financial transaction.)
For me, I don't need the weight or the worry of verifying my coins or bars are "pure", I'd rather just have 6 confirms on my transactions and backups in suitable places as needed. Good luck getting gold across the border, they tend to frown on concentrated wealth moving out of the country.
Me, I'll just bounce my wealth to a secure location and travel with zero problems.
Thanks Bitcoin!