In order for insurance to cover an accident when the insured is not present, there will need to be comprehensive auto coverage. The facts of each such case definitely matter. If the driver is a relative, then most likely the absent insured’s insurance will cover the accident. The driver also needs to have had permission, express or implied, or the insured’s insurance may not cover the claim, unless the vehicle was stolen. Individual insurance companies and policies may vary in regard to these rules.
Liability insurance coverage on a personal auto policy follows the driver no matter whose vehicle is being operated, provided it is an eligible vehicle. All states, except for one (New Hampshire), require at least liability coverage. Liability coverage protects the insured (i.e., follows the driver) when the insured operates a vehicle owned by someone else. In such a situation, they will still usually be covered under their own auto insurance policy. However, the best rule of thumb in looking for coverage under a policy is to begin with the exclusions.
Collision coverage is limited to the actual cash value of the vehicle, and requires a deductible, which is the amount you'll need to pay before receiving benefits. Higher deductibles lower your premium but increase the amount you must pay out of your own pocket if a loss occurs. Ask yourself how much you would be willing to pay on short notice in order to save on your premium, or talk to your agent.
Collision coverage has a deductible, which is the amount you pay before your coverage helps pay for your claim. You can typically choose the amount of your deductible when you buy coverage. So, if you choose a $1,000 deductible and your car is later damaged in a covered accident, you'd have to pay $1,000 toward repair costs. Your collision coverage would help pay the rest, up to your coverage limit.