Gemara

30a (Rav): Pots may not be Kashered for use on Pesach. They must be broken.

Question: He should allow leaving them for use after Pesach, Lo b'Mino (with species other than grain)!

Answer: He decrees lest one use them b'Mino.

45b (Beraisa): One must destroy moldy bread, because one can grind it up and use it to ferment other dough.

(Beraisa): If moldy bread is not proper for people to eat but dogs can eat it, it has Tum'as Ochlim if it is k'Beitzah, and one may burn it [even if it is Terumah] with Tamei [Chametz] on [Erev] Pesach;

(Mishnah): The general rule is, anything [that was] proper for people to eat is Mekabel Tum'ah as long as dogs can eat it.

46a (Mishnah - Ben Beseirah): If one wants to bake a Tamei dough on Yom Tov [of Pesach], he [designates part to be Chalah, and] puts it into cold water to impede Chimutz.

Avodah Zarah 65b (Mishnah): If Yayin Nesech fell onto broken grapes, they are forbidden;

The general rule is, if one benefits from an absorbed taste [of Isur], we forbid [the mixture];

If one does not benefit from an absorbed taste, we permit, such as vinegar that fell on grits.

66a (Abaye): If new wine fell onto grapes, it forbids them b'Mashehu (even if only a drop fell in);

Question (Mishnah): If Yayin Nesech fell onto [broken] grapes [they are forbidden].

Suggestion: The wine forbids b'Nosen Ta'am.

Answer #1: No, the wine forbids b'Mashehu.

Rejection: The Seifa forbids only a beneficial taste. Surely, also the Reisha forbids b'Nosen Ta'am!

Rishonim

Rosh (Avodah Zarah 5:6): The Seifa forbids whatever gives beneficial taste, and permits Nosen Ta'am li'Fgam, e.g. vinegar into grits. Some say that any Isur [that forbids] b'Mashehu, forbids b'Nosen Ta'am li'Fgam. There is no greater Bitul of taste than Mashehu in 1000, and even so the Torah forbids. The same applies to Nosen Ta'am li'Fgam. They support this from our Gemara. It proved that the Mishnah discusses b'Nosen Ta'am, since it permits without Hana'ah. An Isur Mashehu forbids even if it is li'Fgam! This is wrong. The Torah was stringent to forbid b'Mashehu, but only when it is called Isur. If it is Nosen Ta'am li'Fgam, the Isur vanished, like we learn from Nevelah (67b). Also, the Torah forbids b'Mashehu regarding Min b'Mino. There, even one in 1000 the taste is not ruined or Batel. Mino does not harm the taste, and it is not Mevatel it. Nosen Ta'am li'Fgam from the beginning is permitted, for it had no taste. Rather, the Gemara inferred that since the Seifa discusses Nosen Ta'am, also the Reisha does. The Seifa explains the Reisha.

Tosfos (30a DH Lish'hinhu): The Ri was astounded. Even though the taste of Chametz in a pot is Mashehu, for it is rare to use much at once, a Mishnah forbids to be Mevatel Isur l'Chatchilah, even an Isur mid'Rabanan! If not, Chachamim's decree to forbid [mixtures] up to one part in 60 was futile, since one can add and be Mevatel! If wood fell from a tree into an oven on Yom Tov, one may add prepared wood, and burn them, for the Isur of Muktzeh has no source in the Torah. One may not be Mevatel an Isur with a source in the Torah. R. Yosef explains that since there are two reasons to be lenient, i.e. it is Nosen Ta'am li'Fgam and Mashehu b'Eino Mino, we are Mevatel. He must say that the Gemara suggested leaving the Kelim for Eino Mino if Rav permits Nosen Ta'am li'Fgam. The Ri explains that since the pots are of Cheres (earthenware), if they are forbidden, there is no solution. This is considered b'Di'eved. We forbid a pot that is not Ben Yomo, even though there is no solution, because it absorbed much Isur. Here, there is only Mashehu. Since it is not Mino, one may be Mevatel. It is like b'Di'eved.

Ran (top of 8a): Why didn't the Gemara derive from Rav that Nosen Ta'am li'Fgam is forbidden? Some say that we could not learn, because even the lenient opinion permits Nosen Ta'am li'Fgam only for Isurim that forbid through Nosen Ta'am. Chametz forbids b'Mashehu, without concern for Nosen Ta'am, so even li'Fgam is Asur! I disagree. The lenient opinion learns from [the Heter of a] Nevelah that a Ger [Toshav] would not eat. If a Pagum intact Isur is permitted, how can it forbid a mixture?!

Suggestion: If so, why does moldy bread proper only for dogs have Tum'as Ochlim and it must be burned? Since people would not eat it, there should be no Isur! Rather, this implies that even Pagum Chametz is forbidden during Pesach.

Rebuttal (Ran): It has Tum'as Ochlim, for Tum'ah takes effect as long as a dog can eat it. It is burned, for one could grind it up and use it to ferment other doughs (45b). Surely, just like we permit Nosen Ta'am [li'Fgam] regarding other Isurim, also for Chametz. I answer that we didn't infer that Rav forbids Nosen Ta'am li'Fgam because even the lenient opinion permits only b'Di'eved. Even though Rav holds that the only solution is breaking the Kli, this is not like b'Di'eved. I prove this from Chulin 111b. Rav Ami broke a basin in which meat was salted. If this were considered b'Di'eved, he should be permitted to leave it until tomorrow [when the absorptions will be Pagum]! Rather, a basin or pot is not considered b'Di'eved, even if one will have to break it. Rashi says that Rav forbids Nosen Ta'am li'Fgam. This is wrong.

Mordechai (568): If wheat fell into a pit, my Rebbeyim who permit Nosen Ta'am li'Fgam during Pesach permit it. Further, it does not become Chametz as long as it is in cold water, like the Mishnah (46a). Avi ha'Ezri said that all permit the water. Or Zaru'a was unsure about a loaf that fell into a pit, and it cannot give taste to the water. Perhaps this is more stringent than wheat, for the loaf already fermented. If a Chametz dough fell in, it surely gives taste, but we are unsure whether it is li'Fgam, presumably, it is li'Fgam. Also, in such cases we rely on the She'altos, who permits Chametz during Pesach in 60 parts of Heter.

Terumas ha'Deshen (128): Where there is no known custom about Nosen Ta'am li'Fgam during Pesach, we should rule that one who is lenient does not lose, and one who is stringent will be blessed. The Tur writes that Maharam was lenient for others, but stringent for himself. He would tell questioners that Rabanan argue about this. Many refrain by themselves. In Vienna and Krimas, the custom was to permit. In Neostat, the custom was to forbid. Where there is a custom to be stringent, if it is Mashehu and Nosen Ta'am li'Fgam, perhaps the Ge'onim would agree [to permit]. Tosfos (30a) distinguishes like this. It seems that here we do not distinguish. If wheat fell into a pit, the Mordechai says that those who permit Nosen Ta'am li'Fgam permit it. It seems that the wheat was not one part in 60 of the water, and even so those who forbid li'Fgam would forbid.

Poskim

Shulchan Aruch (OC 447:10): Nosen Ta'am li'Fgam is permitted also during Pesach.

Beis Yosef (DH v'Nosen): Tosfos and the Rosh permit Nosen Ta'am li'Fgam even for matters that forbid b'Mashehu. The Mordechai (Pesachim 567) says that R. Yehudah of Paris permitted Nosen Ta'am li'Fgam during Pesach in practice. He brought several Gedolim who agree. Even though he also brought Gedolim who forbid, more agreed.

Magen Avraham (41): Terumas ha'Deshen did not mention smell. Perhaps one may be lenient about Nosen Ta'am li'Fgam and Mashehu regarding smell, since some are lenient [about smell].

Gra (DH Nosen): Nevelah, which is Isur itself, is permitted [when a person would not eat it], and all the more so a mixture of Isur! See YD 103:2. Up to a majority [of Pagum Isur] is permitted. The same applies here.

Mishnah Berurah (96): It is permitted even if there is less than 60 times as much Heter.

Rema: Some are stringent. This is the custom in these lands.

Gra (DH v'Yesh): The stringent opinion learns from 30a. We suggested to leave pots for after Pesach to use only for Eino Mino. B'Mino, the Isur is b'Mashehu, so Nosen Ta'am li'Fgam is forbidden. The first opinion is like Tosfos and the Rosh in Avodah Zarah. We break pots because Ein Mevatlin Isur l'Chatchilah. We can permit b'Eino Mino for it is a second reason to be lenient, in addition to Nosen Ta'am li'Fgam. Alternatively, this is not Mevatel Isur l'Chatchilah, for it is already Nosen Ta'am li'Fgam. Tosfos (Avodah Zarah 76a DH mi'Kan) permits a food [that absorbed Pagum taste], but forbids a pot [in which the absorption became Pagum] because the pot initially had total Isur [but the food absorbed Pagum Isur]. Pots absorbed Chametz of Heter, therefore we suggested leaving them for after Pesach.

Mishnah Berurah (97): Perhaps even if Chametz became totally spoiled after it became forbidden, and it is Asur b'Hana'ah, it cannot be forbid a mixture, for this is not called Hana'ah. It harms the mixture!

Kaf ha'Chayim (227, citing Aruch ha'Shulchan 29): L'Chatchilah one may not cook in a pot that is not Ben Yomo, even before Pesach [on Erev Pesach after midday].

Kaf ha'Chayim (228): In Sefard, for Pesach some adopt all the Rema's stringencies.

Rema (ibid.): Where there is a custom to be stringent, Mashehu and Nosen Ta'am li'Fgam is forbidden.

Beis Yosef (DH veha'Rashba): The Rashba (1:499) says "there is no difference between Nosen Ta'am li'Fgam and Nosen Ta'am li'Shvach regarding an Isur Mashehu. Such an Isur [forbids] not due to taste, rather, due to its severity. If so, it does not matter whether it is li'Shvach or li'Fgam, unless it is ruined so much to become like earth. If so, there is no Isur at all." L'Halachah, since most permit, we follow them.

Bach (5): We forbid Nosen Ta'am li'Fgam even if it is only Mashehu. Likewise, the smell of Chametz is forbidden, like Terumas ha'Deshen (128) said.

Mishnah Berurah (100): One may be lenient about Hana'ah, to sell to a Nochri, for it is also Mashehu. Mishbetzos Zahav (11) is lenient on [Yom Tov Sheni of] the latter Yom Tov if it is Mashehu and Nosen Ta'am li'Fgam, even to eat it.

Kaf ha'Chayim (231): If we forbid Nosen Ta'am li'Fgam, also Hana'ah is forbidden. However, since the Mechaber permits even eating, one may sell the mixture except for the value of the Isur.

Kaf ha'Chayim (236): No one forbids Nosen Ta'am li'Fgam mid'Oraisa. The stringency is because Mashehu forbids, and this is mid'Rabanan! Even those who say Chozer v'Ni'ur (a Isur that was Batel is rejuvenated) during Pesach, even for a wet mixture, if a Pagum taste was Batel before Pesach, we do not say so.

Kaf ha'Chayim (239): Whenever there are more than 60 times as much Heter, this is called Isur Mashehu.