What if the driver is insured but the car is not?

As a rule, insurance follows the vehicle, not the driver, therefore; if the car isn't scheduled on a policy, one should not assume there is any coverage. The only exception would be if a person carries a policy for themselves as a named insured. Say, I had an insurance policy for myself on my own car and I wanted to drive my sister's car. My sister doesn't have her car insured. The LIABILITY portion of my coverage would extend to me as a driver on her vehicle.

Liability covers bodily injury and/or property damage to a third party. So, if I wrecked with another party while driving her uninsured vehicle, my own auto insurance would coverage any physical damage or bodily injury incurred by the party I hit, but that's it. It will not pay to fix my sisters car. It will not pay for any injuries I may have sustained.

You can usually purchase "non-owned" auto physical damage, if you choose. Were this coverage in place, the physical damage to my sisters car would be covered too, had I been driving.