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.
Sounded too good to be true so our friend Google returns
this link. Not sure if this is the same you heard about nor am I sure of what movie is being referred to...
You've all seen the movie where the mountaineer is left hanging in the wind on the end of the rope, his partner unable to help. Our hero inevitably whips off his shoe laces, and uses them to ascend the rope. It makes great footage, but unless you're feeling like James Bond material, or you start using 6 or 7mm accessory cord as shoe laces, I suggest you use a more practical approach.
_________________________
Earth and sky, woods and fields, lakes and rivers, the mountain and the sea, are excellent schoolmasters, and teach some of us more than we can ever learn from books.
John Lubbock