Yes. Liability and coverage for Physical Damage (i.e. Comprehensive and Collision) always follow your car. Plus, if the driver of your car is insured, his/her policy will also be available to cover the cost of damages and injuries.  Unless you have signed an Exclusion for theat driver.

The same rules apply when you borrow someone else’s vehicle; your own insurance follows you no matter whose car you’re driving. But the vehicle owner’s policy is the primary coverage in the event of an accident.