Very scary.
They should have a title somewhere, or could obtain a replacement, right?
I once naively bought a boat with trailer for $120.
They did not have a title either (it was an estate sale). Clearly no foul play, but no title. Neither for boat nor the trailer.
That was a really dumb deal, in retrospect, though I was lucky and was able to recoup my cost by selling to someone else (my contractor). Getting titles for that stuff could cost big bucks and would have been a huge PITA and many frustrating hours. I hope that you will have it better.
i