Typically, no.

It would be up to your GAP policy guidelines. A GAP policy pays the difference between what your physical damage coverage pays (in this case there is no physical damage) and the outstanding balance. When a carrier offers GAP insurance it typically has this set as the first eligibility guideline:

Eligibility only extends to a policy providing comprehensive and collision coverage. Coverage applies only in the event of a premature termination of the loan or lease due to a total loss covered under comprehensive or collision. Coverage does not apply to overdue payments, penalty charges assessed for excessive mileage or excessive wear and tear, etc.

Why would you have a GAP policy without the requisite physical damage coverage? You may be eligible for a refund from your GAP carrier.

Other notable GAP exclusions:

• Overdue lease/loan payments
• Financial penalties imposed under a lease for excessive use
• Security deposits not refunded by the lessor
• Costs for extended warranties, credit life insurance, or other insurance purchased with the loan or lease
• Amounts deducted by the primary insurer for wear and tear, prior damage, towing, and storage
• Carry-over balances from previous loans or leases
• Equipment added to the car by the buyer, meaning that only factory-installed equipment is covered