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Chametz that was disowned by a Jew before Pesach and was found after Pesach:
It is forbidden for all Jews to benefit from Chametz after Pesach if the Chametz had belonged to a Jew before Pesach and never transferred ownership to a gentile, even though it was never actually owned, and transgressed, by a Jew over Pesach. Thus, even if one had performed Bedikas Chametz and had nullified his Chametz before Pesach, any Chametz found in his home [that escaped his Bedika] remains forbidden in benefit for all Jews [if he did not perform Mechiras Chametz], as will be explained in E. Furthermore, even Chametz that was discarded by a Jew before the 6th hour of Erev Pesach into a public for all area, which is even initially permitted to be done in order to avoid the prohibition of Baal Yiraeh and Baal Yimatzeh, remains forbidden in benefit for all Jews after Pesach [if the Chametz is still there]. [This applies even in areas that it is accustomed for everyone to perform Mechiras Chametz.]
If one discarded a box of Chametz in a public area, such as in a street, or in the woods, and came back after Pesach and found the Chametz untouched, it remains forbidden in benefit for all Jews. Furthermore, even if one did not discard the Chametz there, but knows it was discarded by a Jew, it is forbidden in benefit.
 Admur 448:29
 Admur ibid; 437:18 regarding Mapoles; Michaber 448:5 regarding Bittul; Tur in name of Yerushalmi and Rosh; Maharam Chalvah; Peri Chadash 448:5; Elya Raba; P”M 448 A”A 8; Noda Beyehuda; Chasam Sofer; Makor Chaim; See M”B 448:25 Shaar Hatziyon 448:68
Other opinions: Some Poskim rule that if one did Bedika and Bittul to his Chametz before Pesach, then it is permitted in benefit after Pesach even for the person himself. [Opinion brought in Admur that is quoted in Sheiris Yehuda O.C. 14; Chok Yaakov; Mateh Yehuda; Magen Haelef; Rashbatz 199; See M”B ibid and Shaar Hatziyon 448:69]
Chametz found under a Mapoles/mound: Chametz which had a mound of three tefach fall on it before Pesach, and was nullified before the 6th hour as is required, then if after Pesach the mound was removed and the Chametz revealed, then the Chametz is permitted to be eaten. The reason for this is because Chametz which was owned over Pesach is only forbidden due to a fine which the sages fined him for transgressing a Biblical or Rabbinical Baal Yiraeh and Baal Yimatzeh. Thus, since this Chametz that was under the mound one did not transgress anything by owning it, therefore the fine does not apply. However, if at the time that the mound fell one had in mind to remove the mound after Pesach and reacquire the Chametz that was under it, then the Chametz is forbidden in benefit, as explained in chapter 437:18. [Admur 433:34]
 As explained in 445:1
 Admur 448:29-30; Kuntrus Acharon 436:6; See lengthy discussion of Admur on this matter brought in Sheiris Yehuda O.C. 14; M”A 448:8 “The same applies to one who disowned his Chametz”; Peri Chadash 448:5; P”M 448 A”A 8
The reason: Seemingly this is forbidden being that we suspect that he will throw it away with intention to retrieve after Pesach, which invalidates the disowning.
Other opinions: Some Poskim rule that if one disowned his Chametz in a public for all area before Pesach it is permitted in benefit after Pesach even for the person himself. [Opinion brought by Admur, quoted in Sheiris Yehuda O.C. 14; Olas Tamid 447:11 in name of Rikanti 157, brought in P”M ibid]
 As Chametz that was discarded before Pesach was disowned and cannot possibly be included in the sale to the gentile.