In most states, you can have the drivers license suspended until the guilty party pays for damage or sets up a payment plan.
Here is some info on Texas, but your state may vary.
At least make their life difficult so they will get insurance and this won't happen to the next guy.
https://www.txdps.state.tx.us/DriverLicense/CrashSuspension.htm
EDIT: Can't find anything similar to the above site for AZ, but here is some legalese....
http://www.azleg.state.az.us/ars/28/04143.htm