I actually do remember reading about no-VIN Cutlasses sold to racers in the late 80s, here’s some more chat. I think they were more complete than body-in-whites, but not complete or street legal or registerable.
https://classicoldsmobile.com/forums...ag-car-164838/
I think the first car in this video is one of them as well
https://www.youtube.com/watch?v=NC3IweOk2fo