Just as R' Shimon and R' Yehudah disagree whether there is an issur lav on chamietz after chatzos (but before nightfall) on Erev Pesach, they also disagree whether chameitz sh'avar alav hapesach, chameitz which was owned over Pesach, is assur because of an issur d'oraysa or derabbanan (a penalty, knas, for failing to fulfill bal yera'eh). We saw that the Rambam and Ra'avad disagree whether we pasken like R'SH or R"Y on Erev Pesach. However, almost all Rishonim hold that chameitz after Pesach is an issur derabbanan because of the knas of having violated bal yera'ah.
Returning to the Noda B'Yehudah's case, everyone agrees that the Torah does not force yerusha of issur to occur. If a father died r"l during Pesach, no yerusha of his chameitz would take place by his children. If he dies on Erev Pesach after chatzos without doing bittul chameitz, then either already violated bal yera'eh (Rambam's view) and the chameitz is assur, or (acc. to Ra'avad) his children yarshen the chameitz and they violate bal yera'eh at nightfall, and the chameitz is still assur.
Here is where the Noda b'Yehudah comes to the rescue with a chiddush. In many places in shas the gemara debates whether a knas extends to the children of the person who did an issur - e.g. the gemara in Moed Katan discusses whether "kansu b'no acharav" with respect to one who intentionally does work on chol hamoed. The N.B. suggests that perhaps the knas on chameitz applies only one who intentionally violated bal yera'eh, not that chameitz simply by virtue of "avar alav hapesach" becomes a cheftza shel issur. Therefore, if the owner of the chameitz dies, his chameitz cannot be subject to the knas.
The N.B. in the end rejects his own chiddush. It would be too much to summarize the whole pilpul, but one diyuk he makes shows how much can hang on a word of the Rambam. The Rambam writes "chameitz sh'avar alav haPesach assur L'OLAM". The N.B. is medayek from the extra word "l'olam" that even if the ba'al hachameitz dies, the knas of "chameitz sh'avar alav hapesach" still applies.