[DancesWTurtles]

Here is my hunch. It is not a shroud, as in, it is not a piece of cloth that was used at some point to envelope a dead body. But it is not a forgery per se, either.

What do I mean?

I think this is what happened: at some point, after christianism had already settled and there was known iconography, someone made a sculpture of the crucified Jesus. Said sculpture had to be transported somewhere, so someone covered it in cloth, then maybe baled it in with straw or cotton or whatever as protection.

Then it was forgotten for a century or two. Long enough for the sculpture to leave a clear impression on the cloth.

Bam. No need of supernatural whatchamacallits, no need either for advanced forgery techniques. Just a statue and a bit of time.