I had a Honda Dealership sell me a car with a Mazda van as a trade-in. I told them what I thought the "Pay-off" was on the van, but I also told them that I wasn't exactly sure. It turned out, I was off by about $1800. They were in such a rush to get us in their car, and out the door, that they didn't check with the loan company.
They tried to get me to pay the difference, but I had seen them test driving our old van the next day (Saturday), and I believe it was sold that day. Anyway, I told the Salesman that I couldn't afford the extra $1800, and that if they couldn't let the sale go as it was, I'd bring their car back.
Since we were such good customers (had purchased about 5 Hondas in the past 10 years), they decided to let it go. I doubt that they really lost any money in the transaction.
I'm sure most businesses would attempt to collect the monies, but they can usually only go so far, depending on the situation.