Unusual dietary habit--cause for concern?

A friend's cat is feeling bad :(. She is supposed to be going to the vet soon, but I thought I'd check with my friends at PT to see if there are any opinions on this. She is an indoor-only cat and has no problems with getting hairballs up, etc. She is doing No 1 and 2 like she should.

The cat has a very sensitive stomach most of the time (they now are feeding a 'sensitive stomach' formulation of food -- don't remember which brand). She will vomit regularly -- unless (and this is the strange part to me) she has been eating holes in sweaters/afghans. Is there a nutrient deficiency that she is trying to get from the yarn? How should that settle her stomach?

Obviously, the humans of the household are upset that the sweaters and blankets are turning up with holes, oh, and shoe-laces are only half length anymore, too. Any suggestions?