1. Question: According to the Avnei Nezer (Orach Chaim 2:442) Why can a half slave half free person fulfill his mitzvah of listening to shofar on Rosh Hashanah, even if his full self isn’t obligated since a maasah mitzvah, the action if the mitzvah was undeniably done by him listening and part of him is a bar chiyuv, obligated in the mitzvah, however the gemara in Rosh Hashanah 28a says that a person who was a shoteh, halachically insane, and exempt from mitzvos, if he ate matza on Pesach and soon after became normal again he still hasn’t fulfilled the mitzvah and must eat matza again even if the maaseh mitzvah was fulfilled and one who is obligated in the mitzvah is digesting while the obligation is still around, i.e. he became normal that night of Pesach, so why can’t he then fulfill the mitzvah and he does not need to eat matza again to fulfill the mitzva?
A. The Avnei Nezer holds that a half slave half free person cannot blow shofar because you need someone fully obligated in the mitzvah to blow but he can listen because the half which is a Jew is fully listening. This is because the sound of the shofar which is the object of the mitzvah must be done by someone obligated in the mitzvah but the action of the mitzvah does not have to done by a full-fledged Jew.
B. You have to factor in both the action of the mitzvah (maasah mitzvah) and the fulfillment of the mitzvah (kiyum of the mitzvah). The obligation of the mitzvah is only exempted by fulfilling the obligation and fulfilling the obligation is the reason for the removal of the obligation.
Answer: By matza the insane person did a maaseh mitzvah of eating but when he didn’t have an obligation to fulfill the mitzvah therefore when he became normal again he had to eat matza again to perform his maaseh mitzvah when he is obligated. But the half slave half Jew heard a full maaseh mitzvah of shofar being blown and his half that was obligated in that mitzvah fully got the mitzvah.