Since the "shroud" was only woven around 1350, its whereabouts in the century prior to that is hardly a mystery. It didn't exist.

http://skepdic.com/shroud.html

Even if the account of the French knight's encounter with a bit of cloth is true, it provides no evidence whatsoever that it is the same bit of cloth that turned up in Turin (in fact, it couldn't be, because of the carbon date). But then, evidence is not something that bothers the Church too much when it is attesting "miracles".

Now if anyone wants splinters of the True Cross I can let you have them at a very reasonable price.