I have not researched this and do not know traditions of this time, however, I thought this something really wonderful to share.
Why did Jesus fold the linen burial cloth after His resurrection?
The Gospel of John (20: 7) tells us that the napkin, which was
placed over the face of Jesus, was not just thrown aside like the grave
clothes. The Bible takes an entire verse to tell us that the napkin was
neatly folded, and was placed at the head of that stony coffin. Is that
important? You'd better believe it! Is that significant? Absolutely! Is
it really significant? Yes!
In order to understand the significance of the folded napkin, you
have to understand a little bit about Hebrew tradition of that day. The
folded napkin had to do w/ the Master and Servant, and every Jewish boy knew
this tradition. When the servant set the dinner table for the master, he
made sure that it was exactly the way the master wanted it. The table was
furnished perfectly, and then the servant would wait, just out of sight,
until the master had finished eating, and the servant would not dare touch
that table, until the master was finished.
Now if the master was done eating, he would rise from the table,
wipe his fingers, his mouth, and clean his beard, and would wad up that
napkin and toss it onto the table. The servant would then know to clear the
table. For in those days, the wadded napkin meant, "I'm done". But if the
master got up from the table, and folded his napkin, and laid it beside his
plate, the servant would not dare touch the table, because the servant knew
that the folded napkin meant, "I'm not finished yet." The folded napkin
meant, "I'm coming back!"