The purchasing power of inflated, devalued dollars will drop to nil. Eventually the government will issue new currency and your dollar cash, whether in the bank or under the mattress, will be worthless.
Most people will in the same boat when the world goes to a crisp. We'll all be thumbing for a ride down the road to start over from scratch.
“If that is the case with the people who leave their money in the bank, it will also be the case for those that pull their cash out and store it under their mattress.”
You speak as this would be instantaneous. Those with increasingly worthless paper money in hand are much better off than those who have money tied up and unreachable in the bank. There may be some short period of time where the cash-in-hand has some benefit, albeit brief time.