For those in the US, try swapalease.com or leasetrader.com
In the past, I've tried both and had a wonderful experience.
The way this works is that suppose Mr xyz leases a car for 36 months but 5 months into the lease his circumstances change and he wants to offload the car and he advertises the car on one of these websites along with the monthly payment and number of miles allowed per month. If you like the car on the website, you contact Mr xyz and inform him of your interest. He then turns around and contacts the leasing company eg BMW financial and forwards your info to them. Then BMW financial contacts you directly and runs a credit check on you and then transfers the car over to you for the remainder of the lease term.
The car is still under factory warranty. You can negotiate with the original owner (Mr xyz) for some discounts. Some owners are desperate to get rid of the car and agree to your offer.