A world expert on hemoglobin did tests on the Shroud material (multiple tests, multiple techniques) and found breakdown materials from hemoglobin (the tests were not such that they required fresh blood to be valid).
Further study shows that the blood was of type AB, which is the same type as found on another ancient artifact, the Sudarium of Oviedo, which was first mentioned in AD 570.
Incidentally, to answer your question, the Sudarium is celebrated as the cloth wrapped around the face & head of Jesus post-mortem.
And, to answer an unasked question, yeah the burial cloths from a man crucified and with a spear shoved into his heart, just might have some bloodstains on them.
As to address the topic of the thread itself!
I’d love to have that kind of evidence that Jesus existed if for no other reason than to laugh in the face of obnoxious atheists who love waving around their claims that Christ never actually existed.
I think that it’s unwise to base our faith on whether or not a particular bit of cloth is genuine, however. Not that I think many on this thread believe solely because of the shroud, but if it’s ever proven to be not genuine, what damage will it cause to those who are weaker in faith?
And they might not...Jesus' blood was drained...His body was cleaned according to Jewish custom and a hundred pounds of salve was smeared all over his body before any burial clothes came near him...