If you purchase another Hyundai/Kia, yes, you can roll those remaining payments into your new lease. However, you will be paying roughly 80/more in your new lease payment. In your example, you have 11 payments left at $260. Take 260 *11 = 2860. Divide that by 36 months (the longest you really should take a lease out for), and you’ll be paying roughly 80 bucks more for your new car (whatever the new car payment is + 80 for the old car rolled in to your new lease). You’re really just kicking the can down the road doing this, however.
If you go to another brand (BMW, MB, etc…), you can have the dealer cut you a check for the remaining balance + disposition fee (if exists in your contract), and return the car to Hyundai/Kia. Again, however, you’re still adding that to your new monthly payment, so you’re still paying for it in the end.
The third option is to trade the car to a dealership. This doesn’t look likely in your case, however, as your residual is less than your resale value. Dealers aren’t going to give you resale value, however. They use wholesale value. This is the cost it will be to purchase your car at auction. In your case, you owe $16,818 and your KBB value is $11,500. No dealer is going to give you $11,500 however. However, let’s assume they did. You’d then have to roll $5318.00 into your new lease, or roughly $148.00 into your new payment.
Lastly, you can try to sell the car outright, pay HFS off and be done with it. With that said, this isn’t a likely scenario either, as your car is worth less than your payoff.
Ultimately, your best financial course would be just to ride this deal out for another year, and snag a sale next year at model change.