In the event that the other driver is found after fleeing the scene of a car, motorcycle or truck crash, even after your claim is settled with the insurance company, the insurer can and will pursue that driver for reimbursement. This is a procedure known as subrogation. Essentially, they sue the party legally responsible for your injuries on your behalf. This does not mean that your claim can be delayed. Insurers are not allowed to drag out the process of settling with you while they look for or prosecute the responsible party. That is why subrogation allows for the legal process to continue after your claim is technically settled. You are reimbursed and then the insurance company goes after the "bad guys."
Keep in mind that no matter what the circumstances, your insurer will probably try to find reasons to avoid reimbursing you. Much as we like to believe insurance companies have clients’ interests at heart, they are businesses, first and foremost. Businesses must turn profits. Though you should give the police as much descriptive information as possible, be careful about the statements you make to insurance companies and claims adjustors. If these are "recorded statements", you may not be able to change them later, even if you misspeak. You also may not know the extent of your own injuries at the time you make a statement. Once you go on the record, it is very difficult to add information about costs and problems that may surface afterward. However, much as the insurer will try to find ways to pay less, they are bound to pay judgments up to the limits of your coverage.
Like the Dudley Do-Right of cartoon fame, insurance companies can be counted upon to "get their man", if they can find him. Granted, their motivations may be more financial than altruistic, but it’s good to know that in the best case scenario, your insurer will see that a hit and run driver pays for his actions. Most importantly, look out for your own interests after an accident by knowing your rights. You are entitled to the coverage you have purchased. If you have questions or need advice, do not hesitate to seek the guidance of a personal injury attorney with experience in auto accidents and insurance claims.