One solution that i don't see mentioned here is that money simply "wears out": when the money is interacted with (used to pay for something, taken out of/put in storage, examined, etc.) it loses "health", then it can be "redeemed" for new money somewhere if it's not too worn. This is a form of money sink, but a nonobvious one (and really the most accurate, at least for paper/coin money)