It does happen. They sometimes get it caught in the screen and tear it off. Just watch for infection and maybe put a tiny dab of polysporin on it if it is fresh.
As Karma said, they don't grow back - but they can still do all things they "love" to do... I have an old veild that has lost a few of his claws and he is pefectly happy/healthy - he just has extra vines to crawl along so he doesn't have to use his screen much....