Gemara

Tum'ah (of a Mes) pierces through its clothing, but not through ropes less than a Tefach over the Mes more than a Tefach over the Mes.

(Abaye): This is because one is Mevatel clothing on a Mes to the Mes (he decides to leave it on permanently), but one is not Mevatel the ropes!

Shabbos 30b: Every Shabbos David would learn Torah the entire day, so the Satan (angel of death) would be unable to kill him. When David was ascending steps, the Satan removed a step. David fell, ceased learning, and died.

Shlomo sent someone to ask Chachamim what to do, for the body was in the sun. (Perhaps it would rot.)

Chachamim: Put a loaf or child on top of your father. You may move his body together with the loaf or child.

142b (R. Oshaya): If one forgot a wallet in a Chatzer, he puts a loaf or child on top of it and moves the wallet (with the loaf or child).

(Mar Zutra): This is when the Muktzeh was forgotten.

(Rav Ashi): It is forbidden even when it was forgotten. The leniency through a loaf or child applies only to a Mes.

Abaye would put a spoon on top of sheaves (to permit carrying them). Rava would put a knife on top of a (raw, unsalted) dove.

Rav Yosef: Chachamim permitted only for one who forgot, but not to intend to move this way!

Abaye (and Rava) held that really, one may move the sheaves (or dove) by themselves, for one can lie on them (or eat the dove raw). They were stringent, for they are important (lest people learn from them to be lenient).

151a (Mishnah): One may remove the pillow from underneath a Mes, so it will be on the (cold) sand.

Beitzah 21b (Rav Acha bar Yakov): One may not invite a Nochri to eat even on Shabbos, due to wine left in his cup (it is Muktzeh).

Question: One can move it Agav (along with) the cup!

i. (Rava): One may move a pan Agav its ashes, even if there are (Muktzeh) pieces of broken wood on it.

Answer: Here it is forbidden, for the Nochri's leftover wine is Asur b'Hana'ah.

Rishonim

Rambam (Hilchos Shabbos 26:21): If a Mes is in the sun, one puts a loaf or child on it and moves it. The same applies if a fire erupted in the Chatzer in which the Mes is. The Heter to move Agav a loaf or child is only for a Mes, for a person is frantic about his Mes.

Hagahos Maimoniyos (20): This is not only if the Mes is in the sun. It is even if the Mes is on pillows and blankets, so it will not decay. This is only for the sake of the Mes. One may not move it through a loaf or child for the sake of Kohanim or something else (Maharam).

Beis Yosef (OC 311 DH Kasvu): The Kolbo says similarly. We must say that this is when one cannot slip the pillow under the Mes. If one could, he may not move the Mes with it, like it says in Shabbos 151a.

Mordechai (Shabbos 312): R. Avigdor says that a loaf or child is needed only for a naked Mes. One may move a Mes in its clothes Agav its clothes. A proof is from Beitzah

Beis Yosef (DH Kasav): I say that Rashi and the Poskim disagree. If not, they should have specified. The proof from Beitzah is poor. We cannot say that the cup is Batel to the leftover wine, but here the clothing is Batel to the Mes!

Poskim

Shulchan Aruch (OC 311:3): Some say that if one put on a Mes one of the clothes that he is wearing, this is like a loaf or child.

Beis Yosef (ibid.): The Ramban (Toras ha'Adam) said that one may put on a Mes a loaf or child or one of the clothes that he is wearing (to permit moving the Mes). We can say that even though the garment he puts on it is not Batel to the Mes, the Mes' clothing is Batel to it.

Magen Avraham (16): Chulin 125 answers the Beis Yosef. It says about a Mes in its garments, i.e. shrouds, that one is Mevatel clothing on a Mes to the Mes, but one is not Mevatel the ropes! This shows that it depends on intent. Likewise, here one will remove the Mes' garments and clothe it in shrouds.

Chasam Sofer: The Ramban holds that the Mes becomes a bed for the child. One who carries a live child is exempt even for the bed, for the bed is secondary to the child. This is why R. Avigdor brought a proof from leftover wine. He did not simply say that clothes on a Mes are like a loaf or child, because the Mes becomes a bed for a loaf or child, but clothing is Batel to the Mes. Clothing serves the Mes, like a cup serves the leftovers. Meforshim asked about why a loaf or child was needed to move David ha'Melech. He did not die naked, for he was engaging in Torah! I answer that they needed to move him from one Reshus to another. Really, the Heter was only through a child; they said 'or loaf' Agav, for this is usually taught with child regarding a Mes. One who carries a Mes on a bed (in or to Reshus ha'Rabim) is liable even for the bed. It is not Batel to the Mes. It is easily removed, unlike leftover drops of wine or clothes on a Mes. Effort is required to remove them.

Levush: Putting an esteemed garment on the Mes permits moving it.

Question (Malbushei Yom Tov): Why must it be esteemed? Perhaps the words of the Shulchan Aruch misled him.

Answer (Eliyahu Zuta 6): The Beis Yosef asked that the garment should be Batel to the Mes. The Levush answers that an esteemed garment is not Batel. We can answer the question from David. His clothes were Batel to him. Alternatively, the Chachamim who answered Shlomo did not know that he died in his clothes. The Maharal answered that shrouds are Batel to the Mes, but not other garments, for one will remove the Mes' garments and clothe it in shrouds.

Note: Why would the Chachamim think that he died naked? Perhaps 'in the sun' connotes that the body itself is in the sun and will rot quickly. Perhaps Shlomo told the Shali'ach not to say for whom he asks, lest the disgrace of his father lying in the sun become known.

Magen Avraham (15): The same applies to any Kli she'Melachto l'Heter (its primary use is permitted on Shabbos. One may put it on a Mes to permit moving it.)

Eshel Avraham: Abaye and Rava used other Kelim to permit using Muktzeh. He held that that a loaf or child permits other Muktzeh. In any case we learn that for a Mes, the Heter is not only through a loaf or child.

Note: It seems that he refers to Rav Yosef, who thought that Abaye and Rava permit due to the utensil on the Muktzeh. Surely Abaye and Rava agree, for if not, perhaps one who sees them will permit moving Muktzeh through a utensil! Eshel Avraham concludes 'in any case we learn that for a Mes...', because Rav Ashi, who is Basra, holds that the Heter through a loaf or child applies only to a Mes.

Eshel Avraham: The same applies to any Kli she'Melachto l'Heter. One may not use a Kli she'Melachto l'Isur (its primary use is forbidden on Shabbos), for this is not a need of the Kli itself. Even regarding a Kli she'Melachto l'Heter this is difficult, for one may not move it for no need at all. One may move it only for some need of the day (Taz 308:2). If so, the Heter is only through food or a child!

Note: The Shulchan Aruch (308:4) permits moving a Kli she'Melachto l'Heter only for a need. The Taz (2) explains that if it is needed at some time during the day, one may move it the entire Shabbos.

Mishnah Berurah (15): The Shulchan Aruch permits through the clothes that the Mes was initially wearing, and all the more so if one puts another Kli she'Melachto l'Heter on it.

Bi'ur Halachah (DH Yesh): No one argues with this. This is obvious. Since the Mes is not wearing this garment now, it is like any other Kli she'Melachto l'Heter.

Shulchan Aruch (4): Some say that a loaf or child is needed only for a naked Mes. If the Mes is in its clothes, there is no need for a loaf or child.

Taz (4): Why was a loaf or child needed to move David ha'Melech? One Chacham answered that a king's garments are different, for they are forbidden to other people. A Mishnah teaches that we burn Kelim that a king used. Since others could not use his garments, they did not permit moving him. This is correct.

Bi'ur Halachah (DH Yesh): This answer is difficult. Will we say that the Gemara (which requires a loaf or child for a Mes) discusses a naked Mes?! It is difficult to say that they dressed the Mes in shrouds on Erev Shabbos, but were unable to bury it before Shabbos. Shabbos 142a explicitly says that if one carries a clothed person to Reshus ha'Rabim on Shabbos, he is exempt even for the garments, for they are secondary to the person. Eliyahu Rabah said that this is only for a live person, but garments will be taken off a Mes, so they are not Batel to it. They are like a loaf or child, similar to the Magen Avraham's answer. This is very difficult. When he wears his garment, he needs it to serve his body more than the bier he is on after death (for he cannot lie naked). It is clear from the Gemara that a loaf or child is needed even for a Mes on its bier, even though surely the bed will be removed. One may flip the Mes from bed to bed, but one may not move it due to the bed itself. This shows that even though the bed will be removed, as long as the Mes is on it, it is Batel to the Mes. All the more so, as long as it is wearing its clothes, they are Batel to it, since it needs them. It is unlike a loaf or child.

Kaf ha'Chayim (40): Nezirus Shimshon says that the Shulchan Aruch discusses a garment that one could move without moving the Mes. If he cannot, it is Muktzeh and Batel to the Mes, even if he died on Shabbos.this answers the question from David. It seems that this is only for moving directly. Tiltul Min ha'Tzad, e.g. he holds and pulls the garment until it stretches out, even though this moves the Mes, does not forbid the garment due to Basis. Tiltul Min ha'Tzad for the sake of Heter is permitted. Anyone may benefit from his clothes, since the relatives plan to remove them and dress him in shrouds.

Gra: This Sa'if is like the Ramban (Shabbos 47a), who explains that the ashes are Muktzeh and the Kli (pan) is permitted. We do not say that the Kli is a Basis to Isur (the ashes), for the Kli is important and it is not Batel to ashes.