“They said they would pay off my trade” can sound like the old debt is being taken care of at someone else's expense. What it usually describes is the handling of the payoff. You still need to see how the deal accounts for the money.
The car's value and the loan balance are two different numbers. Suppose your car is worth $15,000 and you owe $21,000. You have $6,000 in negative equity. Selling or trading the car for $15,000 leaves that $6,000 to be addressed.
There is a useful way to turn the question around. If you owed only $10,000 on a car worth $15,000, would you accept $10,000 for it because that would pay off the loan? Probably not. You would want the other $5,000. The amount you owe does not set the value in either direction.
Find where the difference goes
If a lender approves carrying the $6,000 into your next loan, it becomes part of the new amount borrowed. In a simplified example, a $25,000 replacement car plus that $6,000 starts at $31,000 before taxes, fees, cash down, or other adjustments.
The replacement car did not become worth $31,000. Part of that loan belongs to the car you no longer have. You may also pay interest on that carried balance.
A dealer discount or cash down can offset some of it, but the worksheet should show what happened. Keep the replacement vehicle's price, trade allowance, old payoff, and cash contribution visible. A single payment cannot tell you whether the old debt was paid with your cash, absorbed through an actual concession, or added to the new loan.
Use a payoff quote from the lender that is valid for the expected transaction date. A statement balance may not include everything needed to close the account. After the trade, follow up with the old lender until you know the account has been satisfied.
Decide whether replacing the car solves enough
Negative equity does not automatically mean you should keep the vehicle. A car that no longer meets your needs or cannot be depended on may have to go. The question is whether the replacement improves your situation enough to justify carrying the debt forward.
If the current car still works, compare the cost of keeping it for a while with the cost of changing now. Paying down the balance can help, though the car's value may change during that time too. Get updated figures when you are ready to decide.
Be especially careful about repeating the process. Each replacement can carry another piece of an earlier car into the next loan. Eventually the payment you are trying to manage has very little to do with the price you saw on the windshield.
The dealer can arrange a payoff. The numbers have to explain who paid for it.