You seem to have ditched a lot of history and economics classes
When that point is ultimately reached, the government just changes one fiat currency with another, and the cycle continues as before. If inflation is gradual, they don't even need to do that. Replacing the bills with less number of zeroes will suffice in most such cases. For example, if Trump is going to heavily devalue the US dollar during his term, he may decide to replace old and devalued Benjamin Franklin 100 dollar bills with new and precious Donald Trump 1 dollar bills...
In fact, many governments have used this trick in the past
and the people will still believe in the value advertised by the government. Reason is that, this government have all the authority. They decide which one should be use, of course with all the connections and controls, they can easily implement this kind of stuff and people will just have to follow. Well they are the one who give these people power to decide for the country anyway. I bet every citizen will believe if someone pass this kind of bill and is approved . After all citizen have to follow the set of rules implemented by its government.