The person that was at fault must still pay for the other driver's property damage, even though that driver did not have a license or insurance. The person without insurance could also recover medical bills and lost income if they can prove he/she were injured in the accident, but because he/she did not have liability insurance, he/she cannot recover pain and suffering damages. The fact that the driver gave wrong information at the scene may reflect poorly on his/her credibility if that is an issue.
The lack of a driver's license will not change the liability. The lack of insurance would only stop the non at fault driver from making a claim for non-economic damages (pain and suffering). So to answer your question: the driver without a license and insurance can still be paid.
In California, a not-at-fault driver who has no liability insurance is entitled to reasonable and necessary medical bills, property damage repair and other quantifiable damages. However, he or she is NOT entitled to pain and suffering. This all comes under what we call Prop 213 cases (a law enacted in 1996 which prevents people from, among other things, collecting for pain and suffering if they have no liability insurance).
Please see the link below for more details and some relevant links.
You should still seek the advice of a personal injury attorney who can address your specific issues and facts.