Gemara

Sanhedrin 46b - Question: Is the reason for burial to avoid disgrace (of a rotting corpse), or for atonement?

The answer teaches about one who asked (before he died) not to be buried: if we are concerned for disgrace, we do not comply. If it is for atonement, since he does not want it, we honor his request.

Nazir 43b (Beraisa): A Kohen may not be Mitamei (become Tamei) for Ever Min ha'Chai (a limb that separated in the lifetime) of his father, but he may return for a bone the size of a barley seed.

This is like R. Yehudah. Chachamim permit only for an intact Mes;

(Beraisa - R. Yehudah): "He will be Mitamei for her (his sister)", but not for her limbs. He may be Mitamei for a limb that separated after death, but not for Ever Min ha'Chai.

(Beraisa): R. Yitzchak's father died in Ninzak. R. Yitzchak did not hear until three years later. R. Yehoshua ben Elisha and four Chachamim expounded "for his father" - he may be Mitamei only for an intact Mes.

Kesuvos 20b (R. Chanina): Mounds that are close to the city or the road are Tamei, because lepers bury in them limbs that fell off.

Bava Kama 85a: To evaluate pain, we assess how much one would want to receive to have his limb cut off if it was dangling (and useless).

Objection: That is too much, for it also entails embarrassment that his limb will be fed to dogs!

Gitin 21a: If one wrote a Get on a slave's hand, he must give the entire slave. He cannot cut off his hand!

Rishonim

Rif and Rosh (Hilchos Tum'ah 1b and 7) and Rambam (Hilchos Evel 2:14): A Kohen may not be Mitamei for Ever Min ha'Chai of his father.

Yad ha'Melech: We must say that one must bury Ever Min ha'Chai. If not, we need not teach that a Kohen does not become Tamei for it! Bereishis Rabah (60) learns from "Yiftach was buried in the cities of Gil'ad" that his limbs fell off in his lifetime, and each was buried where it fell off.

Shevus Yakov: We could also learn from Kesuvos 20b, which says that lepers bury their limbs in mounds. However, these are not proofs, for perhaps there is no Chiyuv to bury them. Sanhedrin 46b discusses whether we must bury to avoid disgrace, or for atonement. Surely atonement does not apply to Ever Min ha'Chai, for one feels nothing when his limb is buried. Also disgrace does not apply, for he is alive. We must say so, for if not, this would be another difference between the reasons! Bava Kama 85a proves that there is no Chiyuv. It assumes that a limb cut off will be fed to dogs! However, one must put the limb in a place where where Kohanim will not become Tamei through it.

Tzitz Eliezer (10:25:8): The Gemara, Rambam and Shulchan Aruch do not explicitly discuss whether one must bury Ever Min ha'Chai. There is no proof from Yiftach. We do not learn Halachos from Agadata, especially one that was not brought in the Gemara! Also Kesuvos 20b is no proof. Rashi explains that the limbs are Tamei like Ever Min ha'Mes. I.e. we bury limbs (not because it is a Mitzvah, rather,) so Kohanim will not become Tamei through them. If so, perhaps the Rambam holds that burying Ever Min ha'Chai is not a Mitzvah! One might have thought that a Kohen buries his father's limbs not due to a Mitzvah to bury, rather, lest they be Metamei others, and any way that will prevent this suffices! The Gemara did not say that the reasons for burial differ about Ever Min ha'Chai, but this is not a proof. Perhaps "bury him" applies even to Ever Min ha'Chai, and the Gemara merely investigated the law of one who asked not to be buried. The Radvaz supports this. However, the verse discusses a Mes, and we cannot learn from it to Ever Min ha'Chai. Teshuvos Maharil Diskin (Kuntres Acharon 185) adds that if there were a Mitzvah to bury due to Tum'ah, why did the Gemara ask whether burial is due to disgrace or Kaparah?! Rather, it is only a custom to bury Ever Min ha'Chai. There is a Chiyuv to bury limbs due to the custom. Also, one may benefit from the limbs, for if not there would be a Chiyuv to bury them like we bury Isurei Hana'ah. Also Pachad Yitzchak (Kevuras Karka) says that it is only a custom to bury Ever Min ha'Chai. If one fears that it is dangerous to bury it, he need not fulfill the custom.

Rosh (Nazir 43b DH Aval): R. Yehudah permits Tum'as Kohen for Ever Min ha'Mes only if he already became Tamei for the rest of the body. There is no reason to permit Tum'ah for it more than for Ever Min ha'Chai

Rashi (Gitin 21b DH Lo): One may not cut off his slave's hand, for he may not hit his slave. We find that a slave goes free if his master cut off a limb!

Rashash: Why didn't Rashi say that if he cuts offf the hand, the slave is free, and the master may not steal the hand with the Get? It is not Asur b'Hana'ah (and hence Hefker). One may benefit from Ever Min ha'Chai (Bava Kama 85a)! Perhaps because the slave goes free due to loss of his hand, the master receives the hand.

NOTE: Rashi and the Rashash did not say that if he cuts off the hand, it is Ever Min ha'Chai and it must be buried.

Poskim

Noda b'Yehudah (2 YD 209): A case occurred in which a Kohen's legs were cut off, and enough flesh remained to be Metamei Kohanim. He wanted to keep them to arouse people's mercy for him. Surely this is forbidden, just like a Kohen may not become Tamei for his father's (or any other relative's) Ever Min ha'Chai, or his own. Tum'as Kohen is permitted only for a Mes, for then there is a Mitzvah to bury it. We bury Ever Min ha'Chai only to avoid Tum'ah.

Igros Moshe (YD 1:231): According to the Noda b'Yehudah, since flesh from a living person is not Tamei, there is no need to bury it. However, if there is no Mitzvah, why does R. Yehudah need a verse to teach that a Kohen may not become Tamei for it?! The Yerushalmi says that R. Yehudah permits a Kohen to be Mitamei for it; he must hold that there is a Mitzvah to bury it. The Rosh says that (the Bavli holds that) R. Yehudah forbids Tum'as Kohen for Ever Min ha'Mes (without the body), for it is no better than Ever Min ha'Chai. The Rosh must hold that R. Yehudah obligates burying Ever Min ha'Chai, for if not the difference is obvious! We may learn from R. Yehudah to Chachamim. The Noda b'Yehudah is difficult. Since one must bury Ever Min ha'Chai, one must bury also flesh from a Chai.

Tzitz Eliezer (ibid.): It was so obvious to the Noda b'Yehudah that there is no Mitzvah that he saw no need to bring a proof. Poskim argue about whether or not there is a custom to bury Ever Min ha'Chai in a cemetery. When needed, one may keep it in a room (where it would not be Metamei Kohanim). One may use it for medical research or practice; this is not a disgrace. Afterwards, it should not be thrown out disgracefully.

Rashash (Medrash Eichah Petichah 42): The Medrash says that when Yirmeyahu returned to Eretz Yisrael, he found cut offf fingers and kissed them and put them in his Talis. A Kohen may not become Tamei for Ever Min ha'Chai! The Heter of Mes Mitzvah applies only to the head and majority, and if so he should have buried them; also, the Poskim connote that we do not bury Ever Min ha'Chai! We must say that they were partial fingers.

NOTE: Ha'Radal (79) suggests that they were Ever Min ha'Mes; regarding a Mes Mitzvah, we become Tamei again even for limbs. (Perhaps he waited to bury each finger with the person it came from; he knew this through Ru'ach ha'Kodesh.)

Gesher ha'Chayim (1:16:2:2,3): Even though we bury Ever Min ha'Chai only due to concern for Tum'ah, if the person already bought a grave, we bury it there, and when he dies, we bury him near the limb.

Mishneh Halachos (16:113): Ha'Emek She'elah (YD 97) discusses a man who lost a finger, moved, and died. The father wanted them to send his son's finger to be buried with him (so that he will not lack a limb at the time of Techiyas ha'Mesim), The Radvaz (8:197) teaches that if a Mes is moved, if anything remains in the old grave, the person will be lacking until the remnant rolls to Yerushalayim. Rashi (Pesachim Sof 68a) says that Mesim will be revived the way they died (i.e. were buried), and afterwards Hash-m will heal them. In some places, the custom is to cast baby teeth in a mousehole. This is because the entire body, including teeth, must be buried. Even though the Noda b'Yehudah held that a limb need not be buried, he came to his son in a dream and asked him to bring his tooth from a certain place to his grave. The son was astounded to find the tooth in that place.