Chullin 129 - Dangling Limb of a Person
One day Rabbi Assi did not go to the study hall. Afterwards, he met Rabbi Zeira and asked him, "What was said in the study hall?" Rabbi Zeira answered, "And what's your problem?" Rabbi Assi said, "We learned that if one first has a thought to eat a piece of meat, and then cuts it off a limb severed from a live animal, that piece of meat accepts ritual impurity of foods. But why? It was not prepared for impurity by becoming wet!" However, Rabbi Assi was missing another principle: "If something can acquire a severe impurity that can even make people impure, it does not need preparation to become impure itself."
The limb or flesh that are dangling from a living person are ritually pure: since the person is still alive, they are considered part of him. If he dies, the flesh is pure, but the limb conveys impurity as a limb from a live person, not a dead person. What's the difference, if both have the impurity of the dead? In the first case, a small piece of flesh from this limb does not convey impurity, but in the second it does.
Art: Arie de Vois - The Wanton Student