What is the blue book value? The insurance company will probably only pay blue book. So if it is less then they will make a deal with the Lease company. They have lawyers for that.
I have only had a few leased vehicles but in each case the dealership had a Gap Insurance quote ready to be added to the lease cost. The full term cost of the gap was added to the lease cost and amortized with the lease cost.
This is really critical now as values of used or leased cars are way up with blue Book values lagging with reported sales.