The cloth "around" his face in the original Greek actually is better translated as "encircling" or "about" his face. This describes a cloth twirled like a kerchief and used under the chin, around the head, tied above the crown of the head to keep the jaw closed.
In modern burials, morticians sew the gums of the upper mandible to the lower mandible behind the teeth to achieve this same result. It would not be a good look for the deceased’s mouth to sudden drop open and gape during an open coffin viewing.
In Jesus’ tomb, it was noted that the sudarium, literally a sweat cloth that would be rolled and then tied around the forehead to keep sweat from dripping into a worker’s eyes, was found rolled up, separate from the rest of the grave clothes. This was of significance to the New Testament chroniclers because to them it indicated that Jesus walked away, reached up, pulled off that jaw closure binding from about his face and dropped it near the entrance of the tomb on his way out. It was an important detail for them. They wrote it down after passing it down orally for almost two centuries.
Some translation of the Bible call it a napkin… trying to relate the size of the cloth to cloths people knew in their daily lives. A napkin in that day and age was an apron, a covering used in a kitchen to protect clothing, fairly large, as was the sudarium at 33"X 21" napkin would be an excellent choice of words in olde English in the 15th Century to select describing an apron cloth of that size. Note that the distance across the diagonal of the cloth is 39" and would be more than enough to provide the binding for keeping the jaw closed in death.
The Sudarium, the one supposedly found in the tomb, still exists today and is on display in the Cámara Santa of the Cathedral of San Salvador, Oviedo, Spain. It has been there since 600AD.
The Sudarium of Oviedo