Q) If I sold my chometz to a non-Jew do I still need to destroy chometz that I found on Pesach?
A) The default position regarding one who found chometz (that he owns) in his domain on Pesach is that the chometz must be destroyed as soon as is practically possible; namely, if the chometz is found on chol hamo’ed it must be destroyed immediately, and if it is found on Yom Tov it must be covered until the end of Yom Tov and then destroyed immediately (see Shulchan Aruch OC 446:1).
Nowadays, many, if not most people sell before Pesach all chometz that they are not intending to destroy. The sale usually includes all chometz that one owns even if it is not known about and even if it is not designated in the sale. This means that if one finds chometz in his house on Pesach (that belonged to him before Pesach) technically the chometz belongs to the non-Jew who purchased all one’s chometz. Although one may not have in his domain even chometz that belongs to a non-Jew (without erecting a mechitza as a visible reminder that the chometz may not be eaten) there should presumably be no reason to destroy the chometz – as it anyway has been sold to a non-Jew and poses no problem of bal yero’eh?
Rav Tzvi Pesach Frank (Mikro’ei Kodesh Pesach vol. 1, 74) discussing this situation where one sold his chometz to a non-Jew before Pesach and subsequently discovered in his house chometz on Pesach, rules that there is no need to destroy the chometz; instead one should put it away with the rest of the chometz that was sold to the non-Jew.