Whether or not you have to reimburse your health insurance depends largely on whether or not your insurance is governed by state or federal law.
Valuing a claim is a complex process. Many insurance companies use a software program named Colossus to help them determine the value of your claim.
When the at-fault party is uninsured, you have the option to file a civil lawsuit against their personal assets or file a claim with the crime victims compensation fund.
If you were injured in the U.S., you may make a claim in the U.S. regardless of legal status.