A Jew’s Chometz
1. It is forbidden to benefit from chometz that was owned by a Jew on Pesach (שו"ע סי' תמ"ח ס"ג ). This is a penalty from Chazal for transgressing the issurim of בל יראה ובל ימצא (מ"ב סק"ז ).
2. This penalty forbids the chometz to everyone, not just its owner; otherwise, it would be simple to circumvent it (ערו"ה ס"ז )
3. The chometz in an irreligious Jew's store is considered chometz she'avar alav haPesach and one may not purchase it. However, one may purchase non-chometz goods from his store.
A Non-Jew's Chometz
4. Chometz that was owned by a non-Jew on Pesach may even be eaten (שו"ע שם ס"א ).
5. Therefore, if a Jew gave a non-Jew chometz before Pesach without any stipulations or made a true sale of chometz to a non-Jew, it is not called chometz she'avar alav haPesach, even if the Jew knew the non-Jew would not touch the chometz and return it after Pesach (שו"ע תמ"ח ס"ג ).
Hefker
6. Chometz that was truly hefker on Pesach may be eaten after Pesach (מ"ב סי' תמ"ח סק"ב ). However, if one made his chometz hefker planning on repossessing it after Pesach, it was not truly hefker (מ"ב סי' תמ"ה סקי"ח ) and it is forbidden after Pesach.
Chometz of Tzedakah
7. Q: The person in charge of a certain organization which distributes food to the needy forgot to include the organization's warehouse in his chometz sale. What is the status of that chometz after Pesach?
8. A: The gabbai did not personally transgress בל יראה ובל ימצא , since the chometz was not his, nor was he responsible for it (שו"ע חו"מ סי' ש"א ס"ו ) when it was not designated for specific poor people. The poor did not transgress since the chometz was not theirs. Therefore, the chometz may be eaten (שו"ת חלקת יואב ח"א או"ח סי' י"ט ).
Doubt
9. Some poskim are meikel in a case where one is unsure if a particular chometz item was owned by a Jew on Pesach or not because it is a safeik d'rabanan (פמ"ג יו"ד סי' צ"ט שפ"ד סקי"ז ). However, the poskim debate whether one may only derive benefit from the chometz without eating it or whether one may actually eat it (חוק יעקב סי' תמ"ט, ישועות יעקב שם, ועי' באריכות שדי חמד מערכת חמץ ומצה סי' ח' אות ל').
10. If one is uncertain if a sale of chometz was valid or not, some say it is like a case where one is uncertain whether chometz was owned by a Jew on Pesach, and it may even be eaten (שו"ת בית שלמה סי' ס"ב ).
Chometz Mixture
11. There are many food products that have some chometz mixed in. Their halachic status after Pesach if they were owned by a Jew on Pesach depends on the circumstances, as will be explained.
12. Min b'mino, e.g., chometz flour mixed with non-chometz flour, is botul b’rov d’oraisa. Even though one may not retain such a mixture on a d’rabanan level out of concern he might eat it, if he did retain it, it is still mutar after Pesach (מ"ב סי' תמ"ב סק"א ). Some say it is only mutar b’hana'ah (א"ר ס"ס תמ"ז ); others even permit its consumption (מג"א סי' תמ"ז הובא במ"ב שם סקק"ב ). The Sha'ar HaTziyun leans toward the latter (שם ס"ק קפ"ג ).
13. Min b'she'eino mino is only botul in sixty times its volume. Though it may not be eaten on Pesach, if the mixture indeed has sixty times its volume and he retained it throughout Pesach, it may still be eaten afterward. If the volume of the mixture was less than sixty times the chometz, it is assur b’hana'ah even after Pesach (מ"ב סי' תמ"ז סקק"ב ).
14. Less than a kezayis according to many does not transgress בל יראה ובל ימצא in a mixture, even if there was less than sixty times its volume. The poskim argue about its status after Pesach; the Bi'ur Halachah writes "tzarich iyun" (ביאה"ל סי' תמז סי"א ד"ה בין ).
15. Chometz flavor. If chicken soup was cooked with kneidlach and the kneidlach were removed, but the soup does not have sixty times the volume of the kneidlach, the flavor of the kneidlach causes an issur d'oraisa if eaten on Pesach. Accordingly, there is a chiyuv d’rabanan to get rid of it on Pesach. The poskim argue about its status after Pesach. Some hold it is mutar b’hana'ah but should not be eaten; others hold it is assur b’hana'ah. To prevent a great loss, one may be meikel and follow the former opinion (מ"ב סי' תמ"ב סק"א ).
16. Owning "chometz nuksheh" [a chometz mixture that is only partially edible or not chometz gamur (מ"ב שם סק"ב )] over Pesach does not violate בל יראה ובל ימצא . Therefore, after Pesach it is mutar b’hana'ah (שו"ע סי' תמ"ז סי"ב ). Some permit its consumption (מג"א שם סקמ"ו) but most forbid it (מ"ב שם סקק"ז ).