I had this problem with Gunther not that long ago. The tip of his tail opened up.
To keep it on his tail, I wrapped it, then used duct tape to keep it on (being on the end of his tail it would just fly off when he wagged it). Be sure to use cotton padding, I used gauze and wrap that a few times around before putting vetwrap on it (the colored elasticy wrappings). The duct tape would wear off after a couple of days and we would then rewrap.
And I do recommend putting some kind of antibiotic on it. Once wrapped, you could try putting some bitter apple on it to keep her from chewing on it.