As I understand. In state of Texas, there are about 30% of drivers do not have insurabnce. many times someone suggest to pass some law to let policy do something when they find a car driver w/o insurance. But the law never be able to pass the congress(state). The policy do not have the authrity to do anything for the driver w/o insurance.
You may not get anything after you win. So the first is to hire an investigater to search the girl has money.