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there are websites for these situations.
swapalease.com
leasetrade.com
leasetrader.com
First off, why would you expect they would. They will usually give you a couple months extension if you ask them and have a decent reason. You signed a contract fairly recently.
Second, the deals you hear about the job loss programs are for new car purchases now and are a way to get people who are on the fence about buying now due to the economy to come in and buy to drive revenue into new car dealers/move inventory. They are not going to do that with existing loans as the purpose is to get new cars sold.
The lease swap places may be your only bet or get someone to take over the lease that you know.