Wooden headrests were used in the every day life of the Eyptians.
Sometimes they were also placed in a burial to support the head of
the deceased, to keep the body intact and to keep "evil spirits from entering" ("Ancient Egypt"). These headrests tended to act as a sort of pillow, and it is only assumed that a cloth of some sort was placed over the curved area of the headrest.

A terracotta figure of a woman laying on a headrest.