My sister-in-law says her guide told this story during a trip to Israel:
The napkin was actually more like a shawl. It was used by Jewish men around their shoulders, then lifted up as as a head covering during prayer. (Even today, males may not approach the Wailing Wall Jerusalem with uncovered heads).
This is an interesting thing. Apparently, when the shawl was not in use, it was folded. Each family used a distinctive method to fold it. When a person died, the shawl (napkin) was part of their grave cloths.
As the guide told it, when they discovered the grave clothes still inside and the shawl neatly folded, they immediately recognized it as belong to Jesus.
As someone pointed out before, thieves would have not taken the time, nor would have been likely to know the family folding style. It had to have been folded by a family member. And that could only have been Jesus himself.
Contrast that with the resurrection of Lazarus, who came forth still wearing his grave cloths, which included the shawl (napkin).
Well, that's the story she heard in Israel. Is it true? Who knows. But definitely interesting.