I just went through this with my dealer/bank as well.
For trade-in the dealer wanted a 10 day payoff quote from trade-in date.
I traded in on date X, they overnighted the check on X+9, delivered X+10.
My bank said they take 5-7 days to cash the check, so by the time the loan was paid off it was X+17.
In that time I saw my car get listed for sale on the dealer website, and quickly gone.
So they re-sold the car possibly before even mailing the check, let alone before it was cashed hahaha.
End of the day no problem, I was just surprised to see the loan still sitting on my account at the bank that long and wasted time on a number of phone calls since there was a payment due on X+15 that I had to confirm with them not to pay.