The Rishonim disagree over this fundamental question: Is ĥametz that was batel be-shishim before Pesaĥ ĥozer ve-ne’or (“reawakened.” i.e., its nullification is reversed) when Pesaĥ arrives, or does its bitul before Pesaĥ mean that it cannot be ĥozer ve-ne’or? If it is ĥozer ve-ne’or, the entire mixture is rendered forbidden, because during Pesaĥ even a drop of ĥametz is not nullified in any mixture. For example, a crumb of ĥametz that falls into a large dish of cooked meat before Pesaĥ is obviously batel, and this food may even be consumed after midday on the fourteenth of Nisan. The question is whether it is still permissible to eat it after Pesaĥ begins.
Some poskim rule that if ĥametz was batel be-shishim before Pesaĥ, it is considered completely eradicated, and it cannot be ĥozer ve-ne’or on Pesaĥ. Therefore, the entire mixture is permitted for consumption (Rosh, Smag, Tur, and others). Other poskim say that the annulment that takes place before Pesaĥ is not effective; as soon as Pesaĥ begins the ĥametz reawakens, and the entire mixture is rendered forbidden (Rambam, Rashba).
This question has implications for the status of matzot. Occasionally, some water drips on a mound of wheat grains, causing a few of the grains to leaven. It is very difficult to find these grains and remove them from the pile, but it is clear that the kosher wheat grains that did not become ĥametz outnumber the leavened grains by more than sixty-to-one. According to the opinion that ĥametz is ĥozer ve-ne’or, if all the wheat is ground together and matzot are baked from its flour, it will be forbidden to eat them on Pesaĥ, because the drop of ĥametz in it renders all of the matzot forbidden. It is therefore important to make sure that there is not even a single leavened grain in the wheat from which matza is made. However, according to the opinion that ĥametz that is nullified before Pesaĥ is not ĥozer ve-ne’or, the matzot are kosher for Pesaĥ. There is no need to check the wheat kernels one by one in order to remove the leavened ones, because they were already batel be-shishim before Pesaĥ.