Auto loan contracts cannot be transferred to third parties. Some loan contracts allow for sub-leases, in which a new user takes possession of the car and makes the payments. Not all auto loans permit sub-leases.
Sub-leases can be risky for the car's owner, whose name is on the original loan documents. If the new user of the car stops making payments, the owner may find her credit rating damaged and may end up in violation of the terms of the loan contract. Selling the car, rather than sub-leasing it, is a simpler way to transfer payments to a third party. In this instance, the new owner obtains new financing and a new auto loan, then transfers money to the original owner to pay off his loan balance.