This is second hand - but I have read of a climbing accident in which a climber was hanging free after an arrested fall and fashioned prussik sling from his shoelaces, thereby enabling him to ascend the rope to safety. It certainly could not have worked very well, but it evidently worked well enough.

It certainly is easy enough to carry adequate cordage, especially with the newer varieties that are now available, but it i worth thinking of what one might do in desperate circumstances...