Well, the body and blood is considered by evangelicals to be consumed in a spiritual sense, with eating and drinking being metaphors for spiritual receiving. Even if bits of the body and blood were believed to be present there in the cloth with all their spiritual power, it wouldn’t be the shroud itself that was received, but the power of the blood and body as applicable.
“Even if bits of the body and blood were believed to be present there in the cloth”
Consider that even all evangelicals acknowledge that Christ ascended bodily to the right hand of God, so that One of the Three Persons of God actually has a physical body — somewhere, we don’t know where, and He will return. He is Christ in spirit and flesh, even today. So his Blood remaining here on earth is significant — it is in a sense still part of Him.
You could make an argument that his Glorified Body doesn’t concern itself with lost blood, just as we aren’t when we give blood.