The Shulhan Aruch, in Siman 458, records the Halacha of "Hames She’avar Alav Ha’Pesah"-Hames which was left in one’s possession over Pesah. Not only does leaving Hames entail a violation of the Torah prohibition of "Bal Yeraheh U’val Yimaseh," but the Hachamim also instituted a Knas (penalty) that such Hames becomes Assur B’Hana’ah- forbidden to benefit from.
The question is to what extent the Hachamim instituted this penalty. The Shulhan Aruch rules that even Hames left "B’shogeg" (unintentionally) or "B’ones" (accidentally) is forbidden. The Mishna Berura explains that this refers to a case where a person performed the "Bitul Hames" (annulment) by proclaiming "Kol Hamira…" before the holiday. In such a case, he will not violate the Torah prohibition of possessing Hames, since he annulled it and rendered it ownerless. Nevertheless, one is required to search out and burn even Hames which he annulled. If for whatever reason, a person did not burn or otherwise destroy his Hames, it still becomes forbidden after Pesah, even though he did not violate the Torah prohibition of owning Hames. Although there are lenient opinions, this is the Be’ur Halacha’s ruling (458:3), except in a case of Hefsed Merubah (significant loss), in which there is room to be lenient.
Therefore, a person must be scrupulous when buying new Hames after Pesah not to buy from a Jewishly owned store that did not sell its Hames. Even if the owner is totally non-observant, he is still a Jew-no matter what. As the Hachamim said, "a Jew that sins is still a Jew." Conversely, one may not sell his Hames to such a Jew before Pesah. He is not equivalent to a non-Jew, and doing so is a violation of "Lifneh Iver"-placing a stumbling block in front of the blind, as he will now own more forbidden Hames on Pesah than he would have.
SUMMARY
Even if one did Bitul Hames, he must still destroy all Hames in his possession. If he did not, that Hames is forbidden from benefit after Pesah, unless it is a Hefsed Merubah.
One may not buy new Hames after Pesah from Jewish owned stores that did not sell their Hames before Pesah, even if the owner is totally non-observant.
