Gemara

(Beraisa): If one took coals from a pile on Shabbos, he brings a Chatas;

R. Eliezer bar Tzadok says, he brings two Chata'os, for extinguishing the top coals (they are now on bottom) and igniting the lower coals (they are now on top).

Shabbos 123a (Beraisa): If an unripe fig was Tamun (wrapped or buried) in straw, or if a cake was Tamun in coals, one may move it only if it is partially exposed;

R. Eliezer ben Tadai says, one may insert a spindle or Karkar into it (and take it), and the covering falls off by itself.

(Rav Nachman): The Halachah follows R. Eliezer ben Tadai.

Inference: Rav Nachman holds that Tiltul Min ha'Tzad (indirect movement) Lo Shmei Tiltul (is not considered movement, so it is permitted).

Question: He permits to remove a radish that is partially in the ground only if it is right side up (for the top is wider, so he does not move earth when taking it), but not if it is upside down!

Answer: Rav Nachman retracted from that teaching (about the radish).

Rishonim

Rambam (Hilchos Shabbos 25:14): If Heter and Isur (something permitted and forbidden to move, respectively) are next to each other, or one is on or in the other, and when one moves one, the other will move, if he needs the Heter, he may move it, even though this moves the Isur with it. If he needs the Isur, he may not move it with the Heter.

Magid Mishneh: Rashi explains that the fig is unripe, and it was put in the straw to ripen. The straw is Muktzeh for making mud. In Eruvin, Rashi explained that the cake was Tamun in coals that extinguished, for if not, when they are moved around, the upper ones extinguish and the lower ones flare up, like it says in Kerisus. The Rambam explained in Hilchos Shegagos (7:12) that stoking coals causes burning and extinguishing.

Rambam (15): If a fig was Tamun in straw, or a cake was on coals, one may insert a needle or spindle and take them, even though the straw or coals are shaken off on Shabbos when he takes them. Similarly, if a radish or turnip was Tamun in earth, and some of the leaves were exposed, one may remove it through the leaves, even though he moves earth when taking it.

Beis Yosef (YD 311 DH veha'Rambam): The Rambam discusses a cake on coals. He can discuss coals that did not extinguish. Since it is not Tamun in them, he does not stoke them when he removes the cake. He merely moves them, which is Tiltul Min ha'Tzad, which is permitted. The Beraisa does not mean that it is Tamun in coals, rather, on top. Since regarding a fig it needed to say 'Tamun', it said the same regarding a cake.

Beis Yosef (DH v'Chasav): The Tur omitted the law of a cake Tamun in coals, because we must say that they extinguished, therefore it does not teach anything that we do not learn from Peros Tamun in straw.

Question (Tosfos 123a DH Hai): If he intentionally left the radish (in the sand), why does anyone permit when it is right side up? One may not even shake off the Muktzeh. All the more so Tiltul Min ha'Tzad is forbidden! If he forgot it there, why does anyone forbid? One may move it directly if needed, along with Heter, like we say about coins on a pillow (142b). If he needs the place, he moves the pillow when the coins are still on. If a rock is on a barrel in between barrels, one may lift the barrel, (move it away) and tilt it (so the rock will fall). All the more so, Tiltul Min ha'Tzad is permitted!

Answer (Tosfos): He left it with intent to remove it. Even though this is considered like forgetting, like one who did Hatmanah with something that may not be moved on Shabbos (51a). One may shake it off, for he did not leave it for all of Shabbos. Regarding bones and peels, Beis Hillel permit removing the tabletop and shaking them off. In any case, he should not have left it in a way that will require Tiltul Min ha'Tzad. Regarding bones and peels, there was no alternative. Regarding one who did Hatmanah (with something that may not be moved on Shabbos), we are not concerned (that it was improper to do so), for he can shake it off, which is not even Tiltul Min ha'Tzad.

Teshuvas ha'Rosh (22:8, Derech ha'Echad): We find that one may move Isur next to Heter, e.g. a cake Tamun in coals. One may insert a spindle and shake (off the coals). This is only if he forgot. If he placed it (to be there all of Shabbos), the cake becomes a Basis (support) for Isur (and it is forbidden like the Isur). Alternatively, even if he placed it (it is permitted); here is different, for the cake was a Basis only for the sake of baking, (with intent) to remove it.

Poskim

Shulchan Aruch (OC 311:9): Peros Tamun in Muktzeh straw or stubble, one may insert a needle or spindle and take them, and the straw is shaken off automatically.

Beis Yosef (DH Peros): Perhaps the Rosh's latter reasoning helps even for a fig Tamun in straw. The fig does not become a Basis for the straw. It is there only so it will ripen in the straw, and be removed. Perhaps the Poskim hold like this, and therefore they did not distinguish between forgetting and Meni'ach. Perhaps they relied on what they wrote regarding a rock on a barrel, and coins on a pillow, that it is permitted only if he forgot, but not if he was Meni'ach, and all the more so Tiltul Min ha'Tzad is forbidden if he was not Meni'ach. However, since Muktzeh is mid'Rabanan, and we can say that the Poskim are lenient, we rule like this.

Rebuttal (Taz 10): If so, this negates the law of Basis l'Isur! We can say also that a rock on a barrel is not a Basis, for he left it only until he will need to remove it! In Siman 309, the Beis Yosef brought from Terumas ha'Deshen (193) that even if he leaves it temporarily, like people often leave things in a box one on another, it is a Basis, since he knows that the top one will rest on the bottom one on Shabbos. It seems that the Rosh discussed only a cake on coals, for he must take after it cooks, for surely it will be ruined if it is left longer. This does not apply to other cases. The Rema (Sa'if 8) says that Basis l'Isur does not apply to food. This is from the Kolbo. This explains also our Sa'if. Why is he lenient? Tosfos explicitly says that Basis applies to food! On whom will we rely against Tosfos?! It seems that all the Poskim agree that we permit only when he intended to remove it on Shabbos. The normal case of Hatmanas Peros is so they will soften. He will take what he needs when it is proper to eat. The Poskim did not need to say that he will take from them on Shabbos, for Stam, this is the case. The Rema explicitly says so. Even if he left the Peros to be there all of Shabbos, this means that whenever he wants to eat from them, and the rest will remain for another time. This is why there is no Basis regarding food, for surely one intends to eat whenever he wants. Stam, food is destined for this. However, if one decided not to eat them on Shabbos, and did Hatmanah with this intent, even Tiltul Min ha'Tzad is forbidden, like Tosfos says, for this is like a rock on a barrel. The Rosh holds like Sefer ha'Terumah (309), that Meni'ach is not considered like intent to remove it on Shabbos. Also R. Tam and Semag (cited in Beis Yosef) says so. One may rely on them when needed, at least for Tiltul Min ha'Tzad, to move the candelabra in which Neros burned on Shabbos, if no Nochri is around.

Kaf ha'Chayim (66,67): The Acharonim hold that in every case, Basis l'Isur does not apply to food.

Mishnah Berurah (35): Teven is what is the stalk harvested with the grain. Kash is what remains in the ground after harvesting.

Mishnah Berurah (36): If he designated them for animal food or to lie on, it is permitted. In our lands, Stam straw is animal food.

Rema: If they are Tamun in sand or earth, see above (308:38).

Kaf ha'Chayim (78): If one stored lemons in sand, the Rema there permits moving the sand to remove them, and so the Beis Yosef brings here from Shibolei ha'Leket. However, it seems that one should not rely on this, for the Shibolei ha'Leket said that one who does not want to rely on this should stick a knife inside (to remove it).

Mishnah Berurah (38): We discuss earth gathered in the house, which is not considered Muktzeh. Tiltul Min ha'Tzad for the sake of Isur is forbidden. Some people sell on Shabbos and take the money in a Kli or through a garment or drag it with a knife. Aside from the Aveirah of business on Shabbos, they surely transgress Tiltul Min ha'Tzad for the sake of Isur.