First off, you have to have pretty stellar credit to just get a loan for $3500 for a used car. Banks generally don’t care if it’s a collector’s item or not. If that is a red flag, then you might want to avoid selling to anyone who rolls up in anything less than a 2013 Mercedes. And personally, I’m not sure I’d even apply for a loan for a car that is selling for less than half of the average value for it’s year/make/model. $3500? Does it even run? Considering the average price on those is closer to $8900, I really wonder about it’s condition!
Now that I’ve got that off my chest, I’ve bought and sold a couple untitled cars, but they were in jurisdictions that required dual signatures on a bill of sale in order to register the car. In some places, if you have the keys and registration for a car, it’s yours no matter what; no title requirements or other paper trail, totally “finders keepers”. In others, all cars are titled and possession doesn’t always mean ownership.
It depends a bit on how the contract is written, but properly written conditional sales and contracts are generally valid. Whenever I’ve had a car loan, there was a condition that failure to make payments may result in the lender taking possession of the car.