If a "previous" owner had the car stolen and never made a claim on his insurance, and you "purchased" it from the thief (or anyone else who aquired it from the thief), you have a problem.

Why?

One cannot get good title (i.e., right of ownership; not a DMV document) from or through a thief.

If it was stolen and never recovered , but an insurance claim was made and paid, the insurance company--not the previous owner--can take the car back. Why? Because they purchased it and own it when they paid that theft claim.

That being said, two of my racecars never had good title documentation and I am not worried. Why? There was no thief involved.