State laws and insurance policy terms vary however in general insurance follows a car first and driver second. This means the owner of car (your friend) would use their insurance first as the primary insurance coverage and if their coverages were exceeded then your insurance as the driver would be used secondary or if the liability coverages of the owner's policy were exceeded.

So if you backed into a car while driving your friend's car then the other party will normally make a claim with your friend's insurance company which would go against her liability policy. It would be doubtful in a low impact collision that the damages would exceed the friend's coverages but if they did then your insurance policy could possibly be used. Typically, your policy would have no coverage for damage caused while you are in another car (friend's car). So, in this case your Property Damage Liability would not extend to the person's car you hit while driving your friend's car.

As for covering your friend's vehicle, he or she would need collision coverage on it to be covered for the damages that were sustained when you backed into another vehicle. If you had full coverage (collision and comprehensive) then it would not usually extend to cover someone else's vehicle.

If your friend does have to use their own collision coverage to repair their car then their deductible amount would be due. Also since claims will be going against your friend's policy, since you as the driver was at-fault in the accident, then this could affect his or her car insurance rates in the future.