Gemara

(Mishnah): If one was Makdish an empty pit, waste heap, dovecote, tree or field, and afterwards it became full, Me'ilah applies to it, but not to its contents;

R. Yosi says, Me'ilah applies to a field and tree and to what later grows in them, for they are Gidulei (things that grow from) Hekdesh.

Chulin 15b (Rav Papa): Sometimes when one slaughters for a sick person, a healthy person may eat from the meat, for example, one was sick when Shabbos began;

Sometimes when one cooks for a sick person, a healthy person may not eat the food, e.g. he detached gourds.

Nedarim 57b (R. Chanina Trisa'ah): If a Terumah onion was planted and the added growth is more than the bulb, it is permitted.

(R. Yochanan): If a sapling with fruits (within the three years of Orlah) was grafted onto a mature tree, even if the fruits grow 200 times larger, they are forbidden.

Bava Kama 69a (Mishnah #1): People used to mark off Reva'i (fourth-year Peros. They are forbidden outside Yerushalayim without redemption) with clods off earth.

The Tzenu'im (very pious people) would take coins and say 'whatever (Reva'i) was gathered from my field is redeemed on these coins.'

The text should say 'whatever will be gathered is redeemed on these coins.'

Shabbos 51b: One may not crush hail or snow in order to melt it. One may put it in a cup or bowl (to cool off liquid inside).

Beitzah 4b (Rav Masneh): If wood fell from a tree into an oven on Yom Tov, one may add to it a majority of prepared wood and light the wood.

Question: Rav Ashi holds that Davar she'Yesh Lo Matirim (something permitted in another situation) is not Batel, even for an Isur mid'Rabanan!

Answer: That is when the Isur is intact. Here, the Isur is burned.

Rishonim

Rif (Nedarim 19b): The Gemara concludes that Heter growth is Mevatel Isur, even regarding Chasayos (species in which the seed does not disintegrate). This does not apply to Nedarim, because Yesh Lo Matirim.

Rambam (Hilchos Nedarim 5:13): If Reuven said 'these Peros are Korban to me', he is forbidden Giduleihem (even if the seed disintegrates).

Ra'avad (on 16): I do not know why we ever forbid Giduleihem in a species in which the seed disintegrates. We permit Zeh v'Zeh Gorem (something that results from two causes, one of which is forbidden)!

Answer (Kesef Mishneh): We are stringent about Nedarim, for they are like Hekdeshi.

Rosh (Beitzah 3:2): If a Nochri brought a gift to Yisrael, if some of that species is attached, it is forbidden at night bi'Chdei she'Ya'asu (until the time to detach it). Even R. Shimon admits regarding such Muktzeh. Since he did not detach it before Yom Tov, it is like dry figs and raisins.

Rosh: If the species is not available attached, within the Techum it is permitted, and outside the Techum it is forbidden, but at night one need not wait bi'Chdei she'Ya'asu. Chachamim made this stringency only if an Isur Torah was done. When it is available attached, we forbid not only eating, rather, even to move it. Since one may not eat it, it is Muktzeh.

Hagahos Ashri (Chulin 1:19): If there are attached fruits of a species, we forbid fruits detached on Shabbos, lest a Yisrael detach them or tell a Nochri to do so. It is an exertion to dig up turnips or trap fish, so we do not decree about them. However, they are Muktzeh unless he expected a Nochri to pick them. Similarly, juice that exuded from fruits is forbidden lest one squeeze, even if the fruits were intended to be eaten.

Tosfos (Bava Kama 69a DH Kol ha'Nilkat): According to the opinion that the Tzenu'im redeemed the Revai while it was attached, this did not help for what grew afterwards (before it was picked). They fixed (redeemed) what they could. Also, perhaps the additional growth was Batel in the majority. Even though Davar she'Yesh Lo Matirim is not Batel even in 1000, mid'Oraisa it is Batel.

Rebuttal (Gra OC 320:2 DH v'Afilu): What piety is it to cause people to transgress an Isur mid'Rabanan? It would be better to mark it off, so people will not take it! (Rather, it is Batel. See below OC 320:2.)

Poskim

Rema (OC 318:2): If on Shabbos one detached, for a (mortally sick) Choleh, Peros that were attached, even if he was sick from before Shabbos, a healthy person may not eat them on Shabbos, because they constantly grow on Shabbos.

Beis Yosef (DH v'Im): According to the Rosh, Magid Mishneh and the Rashba's Rebbi, why is an animal different than something attached? Just like if a Nochri brought a gift, we say that since he should have detached them from before Shabbos, but he did not, he took his mind off it so it is Muktzeh, we should similarly forbid an animal slaughtered for a Choleh on Shabbos. It seems that they hold that we do not forbid a gift that a Nochri brought due to Muktzeh, rather, due to a decree lest one detach, like the first answer in Tosfos in Beitzah (3a DH Gezeirah). And even if you will say that it is due to Muktzeh, we can say that it is like R. Yehudah, who forbids Muktzeh, and the Rif and Rambam hold that we hold like him regarding Yom Tov, but regarding Shabbos we hold like R. Shimon. Therefore, it is not forbidden due to Muktzeh, only due to the decree lest one detach. However, the Rosh says that only regarding attached Peros we can say that since he did not detach them, he took his mind off it. This does not apply to an animal, which must be slaughtered through an expert using a checked knife. Also, Shechitah is an exertion. Perhaps he wanted to slaughter it, but he did not find an expert or a checked knife or time off from his work to slaughter.

Magen Avraham (4): The Magid Mishneh says that if an animal was slaughtered on Shabbos for one who became sick today, even though it was Muktzeh due to Isur, it is permitted (even to healthy people), because we hold like R. Shimon, who forbids Muktzeh only when he took his mind off it, e.g. a lamp in which he lit (before Shabbos). This is difficult. If so, also Muktzeh of something attached should be permitted if the Peros fell on Shabbos! We can say that the Peros are forbidden lest one detach them. The Beis Yosef gave another reason.

Beis Yosef (DH Kasvu): Orchos Chayim (Hilchos Shabbos 345) says that if one cut an unripe Pri on Shabbos for a Choleh, it is forbidden to healthy people due to Muktzeh. This is even if he was sick before Shabbos, for Hachanah (preparation) does not apply to something attached, for such matters that keep growing. The Ro'oh said so.

Magen Avraham (8): This discusses Peros that were not ripe. If it was fully ripe, we do not say that it keeps growing. If we did, why did the Gemara need to forbid due to a decree lest one detach, or due to Muktzeh? Tosfos (Beitzah 3a DH Gezeirah) struggled with this. Rather, if it was fully ripe, it does not grow more. If so, Hachanah helps. Orchos Chayim derived this. Tosfos (Bava Kama 69a) says that what grew is Batel in the majority. See 320:2 and Tosfos (Beitzah 37b DH l'Isur). This implies that even R. Yehudah holds that it is not Muktzeh, for an animal constantly grows, and one may slaughter it on Yom Tov!

Lev Arye (Chulin 108b DH Emnam): When Chachamim decreed that something is not Batel (Davar she'Yesh Lo Matirim, something important...), if the Isur was never recognized, it can Batel. When mid'Oraisa an Isur is not Batel, this is even if it was never recognized.

Minchas Yitzchak (2:70): According to the Magen Avraham, Tosfos in Bava Kama (who holds that Davar she'Yesh Lo Matirim is not Batel even if it was never recognized) is unlike the Poskim. Based on Lev Arye, we can explain Tosfos like the Ran, that Davar she'Yesh Lo Matirim is not Batel because it is like Min b'Mino, according to the opinion that mid'Oraisa Min b'Mino is never Batel. The Yerushalmi in Pe'ah says that Hekdesh cannot be redeemed onto something attached. I.e. if one redeems the crop but not the land, the crop is forbidden due to a mixture of Gidulei Hekdesh. Even b'Di'eved it is not Batel. This is not due to Ein Mevatlim Isur l'Chatchilah, for b'Di'eved it is Batel. Rather, it is Yesh Lo Matirim. The Gemara in Chulin holds that mid'Oraisa there is Bitul Min b'Mino, therefore also Davar she'Yesh Lo Matirim can be Batel if it was never recognized.

Gra (DH Bein): The Rashba (Chulin 15a DH Aval, citing R. Yonah) says that the Sugyos argue about this (whether food that was not prepared at the start of Shabbos is forbidden due to Muktzeh). The Rif and Rambam connote like R. Yonah and Rosh who permit in every case.

Gra (DH v'Im): In Chulin we forbid what was detached even if there was a Choleh at the start of Shabbos. This is unlike Rashi. According to Rashi, only the Reisha regarding Shechitah discusses when there was a Choleh at the start of Shabbos. Really, it is even regarding detaching. The added growth on Shabbos is not Batel in the Ikar, for it is Davar she'Yesh Lo Matirim, like Tosfos says in Bava Kama. However, based on Siman 320:2 and the Rema (YD 102:4), it is permitted. See the Magen Avraham.

Mishnah Berurah (15): This is when he intended from before Shabbos to detach it on Shabbos. Even so it is forbidden, because Hachanah does not help for something attached that grows constantly, unlike it was fully ripe. If the Choleh became sick on Shabbos, it is forbidden in every case due to Muktzeh. i.

Shulchan Aruch (OC 320:2): Even if grapes were not cut up before Shabbos, if there is wine in the barrel they are in, even though the grapes break open on Shabbos in the barrel, one may drink it on Shabbos, for the juice that leaves the grapes in Batel in the wine.

Taz (3, citing the Mordechai), Magen Avraham (5) and Gra (DH v'Afilu): Even though Davar she'Yesh Lo Matirim is not Batel, since the Isur was never recognized before it became Batel, i.e. it was never called wine, therefore it is permitted.

Gra (DH Misbatel): We learn from Shabbos 51b. Rashi says that the melted snow is forbidden due to Nolad. (It is Batel in the liquid, even though Yesh Lo Matirim, for the Isur was never recognized by itself.)

Gra (DH she'Kol): We learn from Beitzah 4b (that Davar she'Yesh Lo Matirim applies only when the Isur is intact).