Therefore, in such a doomsday situation you have to come up with a situation in which you can trade with people in order to survive. There are two solutions I can come up with, either using precious metals such as Gold & Silver or using Cryptocurrency. Considering that fiat currency is useless, Cryptocurrency might raise in value so that it can be useful as a means of trade as long as the Internet still exists which will most likely be the case.
Even if un-backed fiat currencies are replaced, government issued currencies aren't going away.
I think we'll go back to some variant of the gold standard, where legal tender is pegged to hard commodity value. Decades from now, I could even see government money being backed by BTC.