Insurers don't determine your actual cash value (ACV) settlement based on what you owe, but rather on what the car is worth just prior to the accident. Let's say you owe $20,000 on your new car, but it's only worth about $16,000. If your car is totaled, you might get a settlement check of $16,000 but still owe an additional $4,000 on your loan or lease.
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.
Comprehensive car insurance covers damages from an "act of God," or events that are not caused by a car driving into something else. An "act of God" can include things like damage from a heavy tree branch falling on your car. Since you have no control over when or why a tree branch would fall on your car, this kind of accident would be covered under your comprehensive policy.