There are 2 common injuries to tails in the greyhound business. The first are the tail beaters. Tail beaters are dogs that are so happy they never stop wagging their tails. Even though most crates are about 3 foot deep by 3 foot tall and 32 inches wide this is not enough room for a fullsized greyhound to constantly wag it's tail. Consequently they beat the end off their tails which can make their tail sore and blood starts to splatter everywhere!
No, the cure isn't to beat the dog until he is miserable and won't wag his tail anymore! (that's a joke by the way) The cure is to wrap the end of the tail in cotton and tape so that the dog's tail look a little like a lion's tail. This works fine unless it is a dog that doesn't want a big ball of cotton taped to the end of his tail - then you have a problem because they chew it off.
Then you try to muzzle the dog but nobody want's to keep a muzzle on a dog for 24 hours a day - that is a miserable way to live. If worse comes to worse I have seen people amputate the tail. After scar tissue forms it doesn't become an open wound as easily. You can't cut the tail off because it is like a rudder when the dog is racing and helps them hold the turns at 45 mph!
Then there are dogs that accidentally hit the rail with their tails. I have never figured out how they do that but they do. These dogs come off the track with about the last 3 inches or so of their tail dangling by a nerve usually. If it is a clean cut then you can snip it with scissors and apply antibiotic ointment and cotton and tape. If you keep it clean it will heal in a week to 10 days.
Sometimes they just cut it and you have to go to the vet to amputate it between the vertebrae. A minor surgery but surgery nonetheless. Still only a week to 10 days to heal.