Theft Total Loss
For GAP coverage to provide benefits, your vehicle must be declared a total loss. With vehicle theft, this can happen in two ways. Either the vehicle is stolen and recovered, and the damage it sustained while in the thieves' possession costs enough to consider it a total loss, or the vehicle is stolen and never recovered. In the latter case, your insurance company may impose a waiting period before providing total loss benefits, to see whether the vehicle will turn up first. If you must wait for your insurance benefit, you must wait also for the GAP benefit.
Theft is included in most GAP insurance policies as a standard coverage, so you probably have theft coverage on your GAP policy. However, because each insurer can create its own policies, you should read yours thoroughly to verify that the GAP insurer will pay for theft claims. It may have certain requirements you must satisfy before you receive the benefit. For example, it may require that you file a police report and submit a copy of the report as part of its investigation.
No Comprehensive Coverage
While GAP coverage is designed to pay the difference between a standard insurance settlement and the loan balance, in some cases there may be no underlying insurance protection, either because you never purchased coverage or because your coverage was denied. In these cases, your GAP policy may still pay, though you should read the policy to verify this is the case. Expect the GAP insurer to assign your vehicle a value based on the Kelley Blue Book or other rating bureau's data and pay the difference between that amount and the loan balance. You will not receive enough money to satisfy the loan.
There is a potential for fraud with vehicle theft claims, and insurers know it. Theft claims typically carry more thorough investigations than standard collision or comprehensive claims to minimize the risk of paying a fraudulent claim. If you are convicted, or sometimes even suspected, of stealing your own vehicle or submitting a fraudulent claim, your comprehensive insurer will likely deny your claim, and your GAP insurer is likely to do the same.