Can I trade in my car and use it as a down payment if what I owe exceeds value?

So I’ve had a 2015 Nissan Rouge for 2 years now, it’s setting at 155,000 miles and it’s started giving me a lot of trouble. I was looking to trade in my car and use it as a down payment which I know is possible, but can I still do that if what I owe exceeds the value? Carvana gave me a quote for $2,100 but I still owe $10,000. Could the remaining $8k be added to the new loan so I don’t have to pay a down payment out of pocket? And if so, do most dealerships do that?