In real life, the butcher will use the $100 to buy drugs; and the drug dealer takes the money outside of the little town. You can't have that much debt build-up in this society without previous liquidity, and since liquidity suddenly disappeared, injecting it again will not fully fix the issue.

The reserve banking system works. The problem is that once some people in the chain stop making payments, the whole system collapses (liquidity crisis). A bailout by injecting money is basically all the economic players bailing out the defaulters (ie: people who got services but didn't pay for them).

There are many things that can screw your chain: Imports (negative money), Financial institutions making profits from some schemes without injecting the money back (negative money), or your own citizens taking dollar bills outside the country (again, negative money). Injecting liquidity is not always the answer.