Not a problem at all, as long as you handle it in the right way.
Correct way is for the remaining finance to be paid off over the phone by the purchaser with the owner making the initial call, that is then followed up immediately by a confirmation email from the finance company confirming that they consider the debt settled and have no further interest in the vehicle. Purchaser can then take the car knowing the car is clean, and the ex-owner is sure that the money was legit and the finance company won't come chasing.