First, it's worth remembering that the USD was ostensibly backed by gold up until one generation ago, until the Vietnam War. No kidding. There was some amount of Gold reserve to back dollars, that's why 'Fort Knox' exists. So even the USD was 'just a paper you could trade for gold'! Though really, you couldn't, it was a weird theoretically reality.
Now (and really even then) USD is only as good as the integrity of the US Gov and the Fed. If they crash, USD won't be worth the paper it's printed on. In addition, mechanically, physical currency takes a lot of effort to keep going, and with nobody doing that, well it goes kaput.
Digital currencies rely on various layers of trust: networking, security, legal, financial, regulatory, institutional. If any of those break, we can't use digital currency. Technically, there might be some kind of super cook block-chain that could work without needing the internet, surely, but it's too complicated for regular use as a currency. Maybe for larger transactions between fiefdoms!
But gold and other precious metals would probably be used as s currency until institutional trust could be built back up into institutions so that they could have real fiat currencies.
If knowledge and responsibility were very strongly maintained at the local level, it's entirely possible for regional economies to maintain their own fiats. This requires exceptional knowledge and fiscal/monetary discipline.
If you have a populist, dirtbag leader who can corrupt the integrity of the monetary system, it will destroy everything. This is the source of most hyperinflation scenarios.