The Nodeh B'yehuda (o.c. 20) has a long and elaborate teshuva discussing a situation where a father died after chatzos on erev pesach and had chometz in his possesion. After proving that the children do not inherit this chometz and therefore have no obligation to dispose of it (since it is already assur b'hana'ah so it is not "owned" by the father to pass it on to the children), he discusses whether the children are able to benefit from this chometz after pesach. At first he makes this dependent on whether there is a violation of בל יראה ובל ימצא after chatzos on erev pesach, or only at nightfall. Presumably since the father owned the chometz after chatzos until he died, the chometz would be assur if the father was in violation of בל יראה ובל ימצא. Although most poskim assume that the issur of בל יראה ובל ימצא only begins at night, the nodeh b'yehuda proves that the opinion of the Rambam is that it applies already after chatzos on ereve pesach (this also seems to be the opinion of rashi in pesachi 4a). Even the Ra'avad who disagrees with the rambam would hold that chometz is mutar to derive benefit from (shitas r' shimon that lifnei zemano it is mutar b'hana'ah) until pesach begins, so that the children inherit it and they themselves would be in violation of בל יראה ובל ימצא at nightfall when pesach begins.
But, he then says a big chiddush to be matir the chometz after pesach in this case. He introduces this by pointing to many gemara that address the issue of whether a penalty implemented on the father would apply to his children who inherit from him - what is the din by chometz she'avar alav ha'pesach by the father, is the penalty imposed on the children?
The mishna says that a gazlan can return to a nigzal chometz after pesach (even though it is assur b'hana'ah). The gemara proves from this that by issur hana'ah one can say הרי שלך לפניך. Simply this indicates that it is assur to the nigzal, otherwise there would be no proof to other issur hana'ah (which is assur to everyone). However, the N.B. explains that the chometz is really only assur to the gazlan but mutar to the nigzal. His assumption is that really we are only interested in imposing a penalty on the violater of the issur, but normally we are forced to make it assur to everyone to ensure that the violater will not benefit from the issur by the ability to pass it off to someone else. We can assume that when the violater will not benefit by the ability to pass it off to someone else, the rabbonon wouldn't impose their penalty. Based on this, he explains that the logic of the gemara is that if by issur hana'ah one cannot say הרי שלך לפניך, then the gazlan would benefit by it being mutar to the nigzal because the heter to the nigzal would allow him to return it, which is not the case by other issurei hana'ah. But if by issur hana'ah one can always say הרי שלך לפניך, regardless of whether it would be mutar to the nigzal or assur to the nigzal, the gazlan would be able to return it. Therefore, there is no reason for the chachamim impose their penalty on the nigzal. Normally, they would assur it to everyone to avoid the person who violated the issur from being able to benefit, but here there is no rationale to assur it to the nigzal since even if it is assur to the nigzal (such as other issurei hana'ah) the gazlan can benefit from it by returning it to the nigzal.
Based on this chiddush that if one steals chometz and returns it after pesach, the nigzal can benefit from the chometz and even eat it. From this the N.B. makes a jump and says that if chazal didn't impose a penalty on the nigzal, so too when one owns chometz on pesach and dies, there wouldn't be a penalty imposed on his inheritors. The N.B. suggests a distinction. The chometz that was in the hands of the gazlan never became assur to the nigzal since there was never any rationale to assur it on the nigzal, but the chometz that became assur to everyone in the lifetime of the father, would remain assur even upon the fathers death so that the inheritors cannot benefit from it (which is meduayk in the language of the Rambam - חו"מ א:ד - חמץ שעבר עליו הפסח אסור בהנאה לעולם.
For brevity purposes i am switching to hebrew:
והטעם שהחמירו בחמץ יותר משאר קנסות שקנסו לאסור אף על היורשים, משום דלא נקרא שם האיסור על גוף הדבר כגון במלאכת חוה"מ דלא שייך שם איסור על המלאכה, אבל חמץ אחר הפסח חל שם איסור על החמץ ואינו חוזר להיות מותר במיתת העובר עבירה. אכן, אף שהעלה הנוב"י שבחמץ בפסח קנסו בנו אחריו, מ"מ ס"ל דדין הראשון גבי גזלן שגזל חמץ לפני הפסח ועבר עליו הפסח שאומר לנגזל הרי שלך לפניך, וחידש שמותר בהנאה להנגזל "שהוא אמת וברור". ובסוף התשובה התיר אף להיורשין כל שמת האב קודם הפסח או אפילו בתוך הפסח, שהרי כל הסברא לאסור להיורשין משום דכבר חל הקנס על האב, ומסתברא דלא חל הקנס בתוך הפסח בזמן שהוא אסור בהנאה מדאורייתא, אלא שבכלות הפסח וחוזר מה"ת להיות מותר חל הקנס, וכל שחל רגע אחד לעולם לא פקע. לכן כשמת בתוך הפסח ולעולם לא חל הקנס מותר להיורשין ליהנות ממנו אחר הפסח, אבל כשמת האב שעבר בב"י וב"י רגע אחר הפסח, כבר חל עליו הקנס ואסור להיורשין ליהנות ממנו. עכת"ד הנוב"י