I wouldn't be able to pull it off, but banks do this all the time with cash-substitutes. A small number of people do insist on real cash, but there's a huge amount of credit and debt built on top of a small amount of actual currency.

The banks loan your money out, and charge interest to the borrowers. In return they keep your money safe, and pay you enough interest to encourage you to not switch banks, or demand "real" money.

And governments can go into debt on gold, or US dollars (even if they don't have them, and can't get them in the near future). You can get a complete collapse if the government finds itself bankrupt. In that case, you'll have a bank run, or the IMF will step in, or lenders will take a haircut. It's nothing revolutionary (well, it can start revolutions, but that's not really new).

They can do exactly the same thing with bitcoins.