Kunstler’s World Made by Hand series addresses this, from a standpoint of nothing ever coming back. Basically people could take possession of abandoned properties.
If the grid came back, it would be sporadic and local at first, so no real internet. If a bank or local government was lucky enough to have its systems housed locally then statements could be generated. Then the calculations about what money is actually available (and worth) would have to be made. Unfortunately, most banking and governmental systems are now maintained as “hosted services” by larger software providers, hence internet and cloud storage. Those organizations won’t be coming back anytime soon, so back to Kunstler’s scenario.