Such a system could be easily set up with GNU Taler. I have been thinking about something like that for a while, and the main issue is the legal regulations for the organization that receives the real money. If you are not registered as a bank it is severely restricted where and how you can operate. The laws in Europe are basically ok if you want to have some temporary cashless payment system in a music festival or so, but something permanent and with more money involved is hard to do under the current rules.