A Jew is prohibited to own chametz on Pesach. Thus, he must destroy all his chametz beforehand. If he doesn’t and owns chametz on Pesach, the Mishnah in Pesachim 28a says that the chametz cannot be eaten after Pesach mi’de’rabbanan. (Chametz that belonged to a non-Jew, however, can be eaten after Pesach.)
There seems to be conflicting reasons for this prohibition. The Gemara in Pesachim 29a clearly states that Chazal imposed a k’nas for transgressing bal yeira’eh u’bal yimatzei. However, the Rambam (Hilchos Chametz U’Matzah 1:4) adds that even if a Jew unintentionally or completely by accident (an oneis) owned chametz during Pesach, the food is still prohibited after Pesach so that he will be more be more careful in the future.
In other words, as the Maggid Mishnah points out, even if someone has not transgressed the bal yeira’eh u’bal yimatzei, the chametz is still prohibited. According to the Rambam, the k’nas applies to any chametz on Pesach with which one could, in theory, transgress the aveirah – even if no transgression actually occurred.
Similarly, the Ramban, in Pesachim 31, states explicitly that a person need not actually transgress the prohibition of bal yeira’eh u’bal yimatzei in order for the chametz to become prohibited. This is evident from the fact that chametz owned by a Jew on Pesach is forbidden to everyone afterwards – even though only one person sinned.
The Meiri, in Pesachim, quotes the Chachmei Luneil’s opinion that chametz which a Jew nullified before Pesach is permitted after Pesach since he has not transgressed bal yeira’eh u’bal yimatzei. The Chachmei Luneil stress that one must be certain that the nullification was sincere.
The Meiri, however, disagrees, ruling that the chametz is forbidden after Pesach. He says this is not because the owner violated the rule that one must burn one’s chametz and not rely on nullification alone. Even if the owner was not negligent and merely forgot to burn his chametz in addition to nullifying it, the chametz is still forbidden since one could, in theory, transgress the aveirah with it (which is not the case, for example, if a non-Jew owns the chametz for Pesach).
The Rambam would agree with the Meiri as he also maintains that one need not actually violate bal yeira’eh u’bal yimatzei for the k’nas of Chazal to apply.
Interestingly, even some of the Rishonim who argue that the k’nas only applies to people who transgress bal yeira’eh u’bal yimatzei agree that chametz that was mafkir is forbidden after Pesach. Why? These Rishonim explain that we are concerned that a person won’t be sincere when he is mafkir his chametz.
This is not comparable to someone who sells his chametz to a non-Jew. In that situation, we are not as concerned about that person’s sincerity. Even if a person is not completely sincere regarding a kinyan, the kinyan is still valid and binding. The same cannot be said regarding being mafkir something. There, sincerity matters.