How do you even know the person that is selling the car actually owns it?

If the car is still in the state's system (been registered in the last 7-10 years), the owner can get a lost title from the state. You are way ahead to pay the extra fees and have the owner get a replacement title and have them sign that over.

I would run that vin through the web sight listed earlier before anything else happens. If it comes back as stolen, be prepared to tell the police where the car is currently located, you don't want it sitting on your property. If it comes back as salvaged, it is a parts car. If its not listed as stolen or salvaged, your state may have a process to get a bonded title. Expect to jump through the hoops, its generally not easy, and it probably should not be.

Think of it from the other foot, if your beloved car turns up missing, would you really want to know someone can get it titled in their name easily?

No title means it is a parts car and the price would reflect the value of the parts on it, and it would still have to pass the vin test before I bought it as a parts car.