At first I was picturing one of those fox stoles with the heads still attached, which completely freaked me out. But now that my breathing (and imagination) has returned to normal.
Years ago, my parents had a friend in Israel who spun dog hair into yarn. You obviously need a long haired dog, but as I recall, the yarn was very soft. She didn't shave the dogs or anything, just regularly brushed them.
I wonder if you could do the same thing with persian cats.