Final answer:
The damage to the stop sign would be covered by the insured's liability policy, which is designed to cover damages caused by the policyholder's vehicle to others, including property like a stop sign.
Step-by-step explanation:
When an unoccupied auto coasts down a hill and strikes a stop sign, the damage to the sign would most likely be covered by the insured's liability policy. This policy is designed to cover damages that the policyholder's vehicle causes to others, which in this case includes public property such as a stop sign. Physical damage policies generally cover damage to the insured's own vehicle, not to other property or vehicles. Underinsured motorist policies apply when another driver causes damage but lacks sufficient insurance to cover the costs. The state guarantee insurance fund is typically a last resort for claims that cannot be paid due to an insurance company's insolvency, and would not apply in this situation.