Chametz which a Jew owned on Pesach
If the chometz was not properly disposed of (i.e. burned) and was still under the ownership of a Jew (i.e. was not sold to a gentile) then one would not be permitted to have any ha'nah/benefit from those items. This is colloquially referred to as "chometz sh'evar alav HaPesach" (chometz that was kept over Pesach) and was decreed as a penalty for failure to properly rid oneself of the chometz.
- Although biblically speaking, any chametz which belonged to a Jew on Pesach is permitted to be eaten as soon as Pesach is over, there is a rabbinic prohibition that any chametz which belonged to a Jew on Pesach is forbidden to be eaten or derive benefit forever.
- Chametz of a non-Jew is permitted after Pesach. 
- Chametz of a Jew who "converted" to another religion is forbidden after Pesach.
- If a firm or corporation is owned by Jews and non-Jews and the firm provides food there is a concern of Chametz SheAver Alav HaPesach. 
- Vending machines in public buildings possibly could be stocked by Jews (who didn’t sell their Chametz for Pesach) and one should be concerned about Chametz SheAver Alav HaPesach unless one could ascertain the owner and the one who stocks the machine. 
Post Pesach shopping
- Because of the severity of this decree one has to be somewhat restrained in where he does his post Pesach shopping. If one purchases all of his chometz products from a Jewish supermarket then one need not be concerned as one may assume that all of the chometz was sold over Pesach. The real issue is applicable to those who shop at major chain stores (i.e. Path mark, Shop Rite, Price Choppers, Waldbaums etc.)
- If the majority owner of these stores are Jewish, or even if they are minority owners but are managed by Jews who make the policies, and they don't sell their chometz to a non-Jew then one may not purchase any of the chometz that was in the store over Pesach.
- The problem is that these stores are open throughout Pesach and no Rabbi will be able to convince them to cover up all their chometz sections and hold back sales for an entire week. This is highly impractical as well as financially detrimental to a store that has to service the entire population, gentile customers included. R' Moshe Feinstein zt"l, in addressing the question of whether or not one may buy chometz from Waldbaums after Pesach suggested the following: It should be arranged with the owners of these stores to sell all of their chometz to a non-Jew prior to Pesach even though they will be doing business with that very same chometz. This results in a two fold advantage:
- All the chometz, that was in the store prior to Pesach is not prohibited because of chometz sh'evar alav HaPesach (as it is halachically not owned by a Jew)
- The owner of the store is not transgressing the issur of owning chometz on Pesach (b'al yira'eh ubal y'motzai), which he ordinarily would have been violating countless times with all of the hundreds of chometz products that he ordinarily sells.
When store is owned by non-Jew
- R' Moshe mentions that should the store owner sell any of this chometz over Pesach (which a chain store open over Pesach will invariably end up doing) he would be stealing from the non-Jew. As the chometz in his store for all intents and purpose belongs to the non-Jew who he sold it to. Although stealing from a non-Jew is not permitted, it would be worthy to do such a thing as this way the kosher customers may purchase any item that they desire immediately following Pesach as it was "goyish chometz" over Pesach. Additionally the Jewish store owner will be able to avoid transgressing the prohibition of owning chometz over Pesach many hundreds, if not thousands of times.
- While the Rabbis decreed that one may not use chometz that was Jewish owned over Pesach, the g'zaira does not apply to kitniyos. Therefore, all soda, cereals made with corn flour, and all other legumes are permitted to be purchased wherever one desires without any halachic concerns. Additionally, while certain items such as ketchup, mustard and pickles have vinegar in them which is an ingredient that may be derived from grain, most of the vinegar in the United States is derived from corn and one can assume that this product came from that majority.
- S"A 448:3
- S"A 448:3, Mishna Brurah 448:7 explains that the Rabbis prohibited eating or benefitting from chametz, which was was in the property of a Jew on Pesach, even after Pesach, because he violated Baal Yira'eh.
- S"A 448:1
- Kitzur S"A 114:7
- Rav Schachter on OU Pre-Pesach Webcast 5771 between minutes 100 and 101
- Rav Schachter on OU Pre-Pesach Webcast 5771 between minutes 100:30 and 101:30
- Many issuray d'rabbanon such as chalav akum, bishul akum, pas akum etc. one is permitted to benefit from as opposed to chometz sh'aver alav HaPesach where even ha'nah is prohibited
- This is assuming that the owner of this particular shop can be trusted to do what is halachicaly required
- Minchas Yitzchok:8
- Igros Moshe E.H. 1:7
- Igros Moshe O.C. 1:149, 2:91
- At the time the teshuva was written Waldbaum's was still owned by Julia Waldbaum, a Jewish woman
- Many of the “sugar” cereals such as Honeycombs, Fruity Pebbles etc. use mostly corn flour. However, since many times there is a mixture of wheat flour as well one should check each item before purchasing.
- As opposed to the vinegar used in products that were imported from European countries which mostly use vinegar that came from grains
- As heard from R' Yisroel Belsky Shlita