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Chametz that was sold to a gentile [i.e. Mechiras Chametz]:^[1]

All Chametz that was owned by a gentile over Pesach is permitted to be eaten and benefited from after Pesach.^[2] [Thus, anyone who did Mechiras Chametz before Pesach may eat and benefit without restriction from any Chametz that belonged to them before Pesach and was included in the sale. Nevertheless, some are stringent to negate completely any reliance on the sale, even by a Chametz businesses, and hence do not eat any Chametz after Pesach, unless it was produced afterwards.^[3] Thus, they are particular to only purchase products that were ground into flour after Pesach. Most of Jewry, however, uses this sale literally, to allow their Chametz to remain in their homes over Pesach, begin covered under the sale to the gentile.^[4]] See Chapter 5 Halacha 1 for the full details of this matter!

If the sale was invalid:^[5] If for whatever reason the sale to the gentile was invalid, or one’s Chametz was not included in the sale, then the Chametz retains its Jewish ownership over Pesach, and the Jew transgressed the Biblical prohibition against owning Chametz.^[6] Accordingly, such Chametz is forbidden in benefit for all Jews after Pesach, as explained in A. If, however, the sale was only invalid according to some opinions, the Chametz remains permitted.^[7]

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^[1] Admur 448:2

[2] The Chametz of a gentile is permitted after Pesach as the gentile did not transgress any prohibition by owning it on Pesach, and thus the sages did not prohibit it.

[3] Maaseh Rav that so was custom of Gr”a; Igros Sofrim 48 in name of Rav Akiva Eiger; Orchos Rabbeinu Pesach 19 in name of Chazon Ish and Steipler; Kinyan Torah 7:49; Teshuvos Vehanhagos 1:309; See Piskeiy Teshuvos 448:10

[4] Piskeiy Teshuvos ibid; The Chabad custom is to rely on the sale to sell actual Chametz, and so was practiced by some Gedolei Yisrael, who sold their beer, and would drink it for Havdalah on Motzei Pesach. [See Admur 296:10; Rama 296:2; Mishneh Sachir 118; Otzer Minhagei Chabad Acharon Shel Pesach 31] The Tzemach Tzedek in his old age was accustomed to sell bread for him to eat when Pesach is over. [Otzer Minhagei Chabad p. 80] In the Shtar Mechira of the Rebbe Rashab, actual Chametz was sold.

[5] Admur ibid in Seder Mechira, seemingly retracting from his ruling in 434:15 and 448:8

Opinion of Admur in Shulchan Aruch: In 448:8 Admur rules that so long as one showed intent to sell the Chametz, he no longer transgresses owning it, even if the sale was Halachically invalid for some reason. In his words “Once the Jew has shown before the 6^th hour that he has no intention on having anything to do with the Chametz, then regarding the prohibition of owning Chametz, the Chametz is no longer considered to be his, even though that regarding sale laws, the Chametz has not legally yet been acquired by the gentile, and the Jew may thus go back on the sale. The reason for why showing that one does not want the Chametz suffices to prevent transgressing the prohibition of Baal Yiraeh and Baal Yimatzeh, is because once the 6th hour arrives, since the Chametz is now prohibited in benefit, it automatically becomes ownerless, [as something prohibited in benefit is not considered to have an owner, and thus from a legal standpoint, there is no Jew that owns Chametz once the 6th hour has arrived being that it then becomes prohibited in benefit]. Nevertheless, the Torah decided that any Jew which did not remove the Chametz from his possession before the 6th hour, and did not destroy it after the 6th hour, the Chametz is considered to be his, under his name, in order for him to transgress the prohibition of Baal Yiraeh and Baal Yimatzeh. For this reason if one did an action before the 6th hour showing that he does not want the ownership of this Chametz, then it suffices to remove from himself the prohibition of baal yiraeh and baal yimatzeh when the 6th hour arrives, as through him showing that he does not want to own it he acquires the Chametz to the gentile, even though that from a legal aspect it’s not a completely valid transaction, as explained above.” This idea is repeated also in Admur 434:15 regarding appointing an emissary to nullify the Chametz on one’s behalf “The Chametz that one transgresses Baal Yiraeh and Baal Yimatzeh, is anyways not considered his at all, and one thus only transgresses Baal Yiraeh and Baal Yimatzeh [when he has not disowned it] because the Torah considered the Chametz like it is his, in order for him to be associated with it so he transgress the above prohibition. Therefore, even a mere revelation of one’s opinion, that he reveals even through a messenger that he has no desire at all for the Chametz, suffices to remove himself from having his name associated with it, and he will thus not transgress anything.” So also rules Tzemach Tzedek in Piskeiy Dinim 32; Chok Yaakov 448:13; M”B 448:9; Kaf Hachaim 448:95

[6] The reason: As all Chametz that one plans to sell to the gentile is not included in the Bittul recited on Erev Pesach, and is hence Biblically required to be sold. As since one plans to take back the Chametz after Pesach, the nullification is invalid. [Admur ibid; See Admur 445:2; 436:18-19 and 433:34 regarding Chametz which is placed in a public area, had a mound fall on it, or if a person traveled away from his home, in a way that he is not obligated to remove the Chametz, that nevertheless, if at the time that he placed it in a public area, traveled, or that the Mapoles fell, he had in mind to take back the Chametz after Pesach, then it’s as if the Chametz was never destroyed.] Furthermore, how can Chametz which one plans to sell be included in the Bittul, as how can he disown something that he plans to sell afterwards.

Other Opinions: Some Poskim rule that all Chametz is included in the Bittul, including Chametz that one plans to sell. According to them the sale of Chametz is only Rabbinically required, and is only Rabbinically valid, as it has the status of Harama. [Bechor Shur Pesachim 21a; Toras Hashlamim 6; See Tzemach Tzedek O.C. 48; Likkutei Sichos 16:129; printed in Shulchan Menachem 2:273] According to this opinion, one who does not nullify his Chametz, may not rely on the sale. On the other hand, according to this opinion, one who nullifies his Chametz, may be lenient regarding various matters of the legality of the sale, being it is only Rabbinical. Admur ibid negates their opinion and says the sale is Biblically required, and hence must be valid according to all.

[7] Admur 448:8; Vetzaruch Iyun if this applies even according to the ruling of Admur in Seder Mechira

The reason: If only a disputed form of acquisition was done, and Pesach has already begun, then it is permitted for the Chametz to be eaten after Pesach, and one is not required on Pesach to get the Chametz back from the gentile in order to destroy it, as there is an opinion who holds that only one method of acquisition needs to be done for the gentile to acquire it, either giving the money, or carrying it, and thus since the fine of after Pesach is only Rabbinical, one may be lenient like their opinion, as is always the case by a dispute over a Rabbinical prohibition. [Admur ibid]