Never put money down in the form of a Cap-Cost Reduction. The idea there is simply to lower your monthly by essentially paying a portion of the Captial Expense down up-front. Not a great move. Keep the money in your pocket as the whole idea of a lease is to pay for only what the depreciation you use is.
If you trade or sell or exit your lease early, you won't get that cost reduction down payment back. As already noted, most leases require/build in gap insurance thus if you total the car, you lose the cap cost reduction too.
Leasing is about options and minimizing risks. If the payments are out of ones range doing it this way, they are looking at a car they can't afford or is out of their budget.