If you’re letting someone who is a named driver on your policy (like your child) borrow your car, your auto policy should cover them in case of an accident. When that driver has their own insurance or is uninsured, you will need to consult your policy to see if you are responsible. In general, your provider is the primary source for damages when another driver gets into an accident in your car; your liability insurance covers injuries and damages to other drivers and collision insurance pays to repair vehicle damage.