Keritot, Chapter Three, Mishnah Eight
Rabbi Akiva asks another question to Rabban Gamaliel and Rabbi Joshua.
1) Rabbi Akiva further asked: If a limb hangs loose from the body of a living beast, what is the law?
2) They replied: We have heard nothing about this, but we have heard about a limb hanging loose from the body of a man, that it is clean.
3) And thus those that were afflicted with boils used to do in Jerusalem. He would go on the eve of Pesah to the doctor, and he would cut the limb until only contact of a hairbreadth was left; he then stuck it on a thorn and then tore himself away from it. In this manner both that man and the physician could make their pesah offering.
4) And it seems to us that your case may be derived from this by a kal vehomer.
Section one: A limb removed from a living animal is considered to convey impurity like carrion. Rabbi Akiva asks concerning a case of a limb that is hanging loose from an animal. A sinew or some skin is connecting it to the animal, but the limb will not heal and become fully reattached to the animal. Does such a limb convey impurity even though it is still attached?
Section two: As was the case in yesterdays mishnah, Rabban Gamaliel and Rabbi Joshua do not have a received tradition, but they can again figure out the answer by comparing it to a case for which they do have a tradition. If a person has a limb hanging loose from his body, it does not convey impurity as if it were a dead body.
Section three: They now explain how people would use this halakhah to prevent them from becoming impure on the eve of Pesah, and thereby lose their ability to sacrifice and eat the pesah offering. People who had boils and needed to have a limb removed would go to the doctor. He could not cut off the limb because then he would become impure. To solve this problem, he would cut off most of the limb until it was only connected by a hairbreadth. At this point the limb was still pure. He would then stick the limb on a thorn stuck into the ground like a peg. The person with boils would then rip his own limb off (ouch!). In this way, the doctor would not touch the limb while it was being ripped off. Both the doctor and his patient could then offer their pesah sacrifice that evening.
Section four: From this case we can draw a kal vehomer argument. If the limb hanging from a human body which would convey the more serious impurity of a dead body is pure as long as it is still hanging from the body, all the more so the limb hanging from a live animal, which would have the lesser impurity of carrion, is pure if it is still hanging.