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.
It is obvious that once the government losses control of the economy they are going to try to gain control of it again by backing their currencies with something tangible like gold but at that point in time will their citizens once again trust the government to issue a currency that it will not crash? I say this because most currencies started as being backed by gold, then the backing was withdrawn and they became fiat currencies, what will stop the government to do this again?