You can, but usually there is a limit on the amount they will finance, certain percentage of MSRP. Let's say you are buying a car with MSRP of $20,000, and the lender has a limit of 120% of MSRP. You negotiate a selling price of $18,000, $20,000 out the door. Now you can roll $4,000 of negative equity into the new loan. If you lease - you might be able to roll in more, since you are not paying sales tax on the whole car (in most states).
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