A Greyhound’s tail is long, bony, and whip-like. Because it contains little tissue and the skin is thinly stretched over it, the tail can break open at the end if an enthusiastic tail-wagger (hence the name) severely and repeatedly bangs it against a wall, a cabinet, or some other hard surface.
Because the blood vessels are so close to the surface, it bleeds profusely and blood is thrown everywhere. While the situation is certainly not life-threatening, it sure can require a lot of effort to clean it up.
Bandaging the tail is a challenge, as the bandage can be immediately whipped off an ever-moving slender, tapering tail. If one can get a bandage to stay on, the tail can heal, albeit slowly. However, the next whack on a hard object may break it open again. Sometimes, as a last resort — and this is fairly common — the thin damaged end of the tail has to be amputated to stop the vicious cycle.
If you find yourself with a happy tail situation, here are some instructions on how to create a hopefully successful bandage: Tail bandaging
Greyhound owners with happy-tailed hounds get very adept and creative at bandaging. Ask around and you may be able to find one who has mastered the art. You might want to try this innovative Greyhound tail sling: http://www.featheredgems.com/blog/?p=292