If the US dollar collapses, will a person automatically become poor?

Say you have 1 million dollars in the bank, as of this moment, thats a pretty nice savings account, and gives a person reasonable financial security. However if the US dollar collapses and inflation is rampant like the currency in Zimbabwe, and becomes virtually worthless, does that make a person who has a million dollars in the bank poor since the dollar is no good anymore? Or is there other economic factors that may protect the person, such as higher interest rates?