First thing (maybe there should be a separate thread on this subject) to be suspicious of is when the seller says 'I lost the title' most states have a free vin check on their dmv website, it will not give you any personal information but will tell you the status of the title, ie: stolen or last time it was registered. Ask the seller for a reistration, it will show vin, tile numbers.
The vin is attached to the car with special revits that cannot be attained anywhere except at the factory, and cannot be duplicated (allegedly), a 'retitled' car will have a vin plate riveted to the drivers side A pillar between the door hinges (at least in Florida).
In most cases you can call the local PD and they will tell you if it is stolen.
Now we 'assume' sellers are honest and in most cases they are but we are dealing with 30 year old cars here so protect yourself.
In one instance I was involved in a person borrowed money on a car title, the same day he went to the dmv and got a duplicate title then sold the car to someone a couple days later, that person registered the car and knew nothing about the lein (this was all done before the loan company filed for the lein) until he tried renewed the tag a year later, of course there was a hold on the title and this took almost 2 years to get sorted out. Original owner did several months in jail for fraud and I ended up collecting a bag full of money on storage/investigating fees.
Protect yourself.