I did not want to include this in the previous post so as to not confuse things, but one further point from the Noda b'Yehudah is worth mentioning. Based on his chiddush (see previous post) that the chiyuv of bi’ur chameitz is a chovas hagavra incumbent only upon the owner of chameitz, the Noda b’Yehudah writes that if someone failed to do bi’ur chameitz and dies on Erev Pesach, his/her children can wait and acquire and benefit from that chameitz after Pesach. The owner of the chameitz, not his/her children, is responsible to fulfill tashbisu. Since chameitz cannot be acquired during Pesach, the laws of inheritance do not cause the chameitz to pass to the children on Yom Tov and they violate no issur. The chameitz is not prohibited because of chameitz she’avar alav haPesach because chameiz she’avar alav haPesach is a knas on the owner of chameitz for violating the din d’oraysa of bal yera’eh. The issur of bal yera’eh takes effect only at nightfall of 14 Nisan, at which point the owner of the chameitz was already dead.
The only catch is that chameitz is in effect considered hefker until after Pesach when the yorshim can acquire it. In theory, anyone else can be zocheh in the chameitz as well.