Every situation like this I ever read or heard of, the owner is basically hosed. Though how long they owned it tends to vary of course. Insurance covering it seems to depend how your policy is worded regarding theft. It's weird.
I have actually read several stories like this just different cars. I never saw it end well for the guy who currently owns it though.
It could also be that the car is in bad shape. Shelby frames sell for a decent amount of course though haha. But yeah there could be little left of the car but the body and frame. I know this guy who got a 65 fastback he owned back in a similar story but while it was mostly complete it was rotted on the frame n floor pans and the engine was seized.