If the driver is not licensed, does it affect their ability to file a claim?
I had a friend drive my car and a person ran a stop sign and hit him. The person told his insurance company it was his fault. I found out he doesn't have a license. Does the driver's insurance company ask for their license and would they do a driver's background check?
Most insurance companies do have access to a driver's background when they quote and insure them. Not having a driver's license is usually an issue for insurers but it's not impossible to find insurance for an unlicensed driver, and that seems to be the case in this situation. As long as they honor the claim for hitting your vehicle, it should all work out.
If you have any questions, feel free to ask.