You have to somehow force someone to deposit more into the system if they have a negative balance.
Alternately, you could blacklist defaulters, and create some sort of insurance pool whereby those that lose money through default are compensated. Perhaps a small 0.01% tax on transactions to help compensate for the occasional default?
From a regulatory standpoint, the result resembles a Hawala network of trust, and would be prohibited in the US:
http://www.treasury.gov/resource-center/terrorist-illicit-finance/Documents/FinCEN-Hawala-rpt.pdf