The Mishnah continues with the questions that Rabbi Akiva asked Rabban Gamliel and Rabbi Yehoshua in the marketplace of Emmaus. Here he asks them: What is the law of an "ever hameduldal babehemah" - a dangling limb on an animal? The question deals with the laws of tumah: a limb that was essentially torn from the animal and will never be able to reattach or heal, but it is still dangling and hanging onto it by a little bit of skin - for example, a leg that was torn off and remained hanging by a little skin - is it judged as a detached limb regarding tumah?
Background: The tumah of a limb from a living animal:
An animal that dies is a nevelah, an Av Hatumah. Similarly, if a limb was separated from a living creature - a limb defined as a piece from the animal that includes bone, the flesh surrounding the bone, and the connective tissue - that limb is judged like a nevelah, meaning it is a source of tumah and an Av Hatumah, even though the animal itself is still alive. Regarding this, Rabbi Akiva seeks to know: Is a dangling limb, which is no longer nourished from the body and cannot reattach or heal, already considered like a detached limb that constitutes a source of tumah?
The answer of Rabban Gamliel and Rabbi Yehoshua:
They answered him that they do not have a tradition regarding a dangling limb on an animal, but they do have a tradition regarding a dangling limb on a human: A person whose limb was detached and broken but is still dangling and hanging by a little bit of skin - the limb does not constitute a source of tumah.
The basis for this stems from the verse dealing with tumah that comes from a human: "Adam ki yamut ba'ohel" - a person when he dies in a tent. The person must be dead, and from here it is derived that if the person is alive and something is attached to him, it is not a source of tumah.
An incident with a person afflicted with boils making the pilgrimage:
There is a precedent case for this law: A person who was afflicted with leprosy (known as Hansen's disease), which involves skin lesions and nerve damage - the nerves stop functioning, the limb dries up and has no sensation, and eventually it tears and detaches. Consequently, he finds himself with a dangling limb hanging from his arm. He wishes to go up to Jerusalem and participate in the pilgrimage, but he does not want to be repulsive in the eyes of his fellow Jews; on the other hand, one cannot be tamei and participate in the Pesach sacrifice. And so this poor person stands there, afflicted with boils and his limb falling off, caught between the desire not to be tamei and the desire not to be repulsive.
What would he do?
On the eve of Pesach, he would go to the doctor, who would cut the remainder of the limb until there was nothing left but a tiny bit. The version before us in the Mishnah is "kis'orah", like a barley grain, but the correct text is most likely "kesa'arah" - like a hair, meaning only a hair's breadth of skin remains. (This sounds horrific, and indeed it is; however, for a leprosy patient who has already suffered nerve damage, there was no sensation in that area anyway.)
Afterward, he would attach the limb, which was hanging by a hairbreadth, to a thornbush on the ground.
From there, he would pull himself backward from the bush with all his might, the last piece of skin would tear, and the limb would be left behind on the ground as he separated from it.
After the fact, he was permitted to participate in the Pesach sacrifice and offer it, and so was the doctor who treated him.
The proof from the incident:
Human limbs are a severe source of tumah: just as a corpse is an avi avos hatumah, so too is a limb that is completely severed from a person, and even merely bearing its weight - not to mention touching it - makes a person tamei. Yet here, the limb was not completely severed, and nevertheless that person, who bore the weight of the limb until a moment prior, as well as the doctor, were permitted to partake of the Pesach sacrifice. It emerges that this method - leaving the limb hanging by a hairbreadth and separating from it without touching it or another person afterward - does not transfer any tumah. From here it is clear that a dangling human limb, which is hanging by a hairbreadth, is not a source of tumah.
Rabbi Yehoshua's Kal Vachomer:
From here Rabbi Yehoshua derived a kal vachomer (an a fortiori argument) regarding an animal, since a human is more stringent than an animal in two respects:
Severity of the tumah: Human tumah is more severe, for a human corpse is an avi avos hatumah, whereas a limb severed from a living animal is only an av hatumah.
Susceptibility to tumah: Humans are much more susceptible to contracting tumah, as they can contract tumah even while alive, whereas animals do not contract tumah during their lifetimes at all.
Therefore, if regarding a human, which is more stringent, a dangling limb does not convey tumah, all the more so a dangling limb on an animal does not constitute a source of tumah.
The Halachah:
A limb of any measure, of any size, that was severed from a human or from an animal, as long as it contains bone, sinews, and flesh enveloping it - is a source of tumah, and regarding an animal it has the status of a nevelah. Therefore, it conveys tumah through touch and carrying, and regarding a human, even through an ohel. However, all of this is when it is completely severed, and it does not apply to a dangling limb that is hanging even by merely a strand of skin. This, then, is the law that emerges from the Mishnah.