Abu Waqid al-Laithi told that when the Prophet (ﷺ) came to Medina the people used to cut off camels' humps and cut the fat tails of sheep, so he said, “Whatever is cut off an animal when it is alive is dead* and must not be eaten.” *i.e. it is treated as something which had died a natural death, and therefore may not be lawfully eaten. Tirmidhi and Abu Dawud transmitted it.