No, a forfeiture of your vehicle to the state due to a DUI will not normally be covered by your GAP insurance. GAP insurance pays the loan amount or balance left on a loan after a vehicle's actual cash value (ACV) has been paid out by a primary insurer after a covered loss - such as the car being totaled out in an accident or being stolen and declared a total loss.

A forfeiture or seizure by your state's law enforcement of your vehicle would not count as a covered loss by either your primary insurance provider or your GAP insurance carrier.

If your state's laws allow your car to be seized by the state after a DUI conviction then this would not be a covered loss in which an insurance provider would pay out actual cash value to your (or your lien holder) for the vehicle and thus the difference (or gap) between ACV and your loan balance would not be there for GAP insurance to pay. Instead your whole loan balance would be due.

Many states auction or sell off vehicles they obtained from seizures or forfeitures in which case your lien holder may get some money for your vehicle from the state. Likely this will not be enough to pay off what you owe and thus leaving you to pay off the remaining loan balance.

If your car was forfeited to the state due to a DUI then you should contact the courts involved in your case to find out what they do with seized vehicles and if there will be money going to your lien holder from a sale. You then should also discuss the situation with your lien holder to see what balance you will have left and how to go about paying it off.