What is the status of a dangling limb of an animal? Does it impart ritual impurity like a severed limb? They said to Rabbi Akiva: We have not heard a ruling from our teachers in that specific case, but we have heard with regard to a dangling limb of a person that it is ritually pure. And in this manner would the people who are afflicted with boils (mukei sheḥin) act in Jerusalem: Each would go on the eve of Passover to the doctor, who would cut the affected limb almost completely and leave it connected only by a hairbreadth of flesh (so that neither would be rendered impure by a severed limb). Then the doctor would impale the limb on a thorn attached to the floor or wall and the afflicted would pull away from the thorn, thereby completing the severing. In this manner both that man and the physician could participate in the Passover offering. And it seems to us that your case may be derived from this by a kal va-ḥomer – an a fortiori conclusion.
The term mukei sheḥin refers to people who suffered from a disfiguring disease, although as used in the Mishna, sheḥin includes a number of different ailments. It is possible that the reference here is to leprosy, which is mistakenly given as the common translation for the Biblical tzara’at. Leprosy is an infectious disease whose symptoms involve reactions on the skin, but also attack the nerve fibers, ultimately destroying the nerve cells. This results in a loss of feeling of heat, cold and pain, leading to a situation where the person can injure his limbs, suffer burns and cuts that ultimately affect deep tissue, bones and joints. Severe and prolonged infection can lead to spontaneous amputation of limbs, which may be what is described in the Mishna that inquires about the status of “a limb hanging loose” from a man or an animal.
Rashi explains that the recommended procedure of removing the limb was not performed because of the requirements of the laws of ritual defilement – for the limb remained in a state of purity so long as it was connected to the person. Rather it was done for aesthetic purposes.