If a person did not recite Habdala on Saturday night, does he recite Habdala on Sunday?
A person in this situation does, indeed, recite Habdala on Sunday, though the nature of his recitation depends on whether or not he had eaten anything before Habdala. If he had not eaten anything after Shabbat until he recites Habdala on Sunday, then he recites a regular Habdala, though without the Berachot of "Besamim" and "Boreh Me’oreh Ha’esh." Meaning, he recites the Beracha of "Gefen," followed by "Ha’mabdil," and then drinks the wine.
If, however, the individual ate at some point after Shabbat before he recites Habdala on Sunday, he may not recite the standard Habdala. Since Halacha forbids eating after Shabbat until Habdala, a person who eats forfeits the opportunity to recite an ordinary Habdala. Instead, he recites the Beracha of "Ha’mabdil" without the phrase, "Hashem Melech Ha’olam," followed by the Beracha of "Boreh Peri Ha’gefen," and then drinks the wine.
The exception to this rule is a person who loses an immediate family member, Heaven forbid, during Shabbat. As soon as Shabbat ends, he has the status of "Onen" (a mourner before the burial), which exempts him from all Misva obligations. As such, he cannot recite Habdala until after the burial, as he is not obligated in the Misva of Habdala until that point. One option in this case is for the person to recite Habdala late Shabbat afternoon (after the point of Pelag Ha’minha), before sundown. Halacha allows one to fulfill the obligation of Habdala late Shabbat afternoon, even before Shabbat has ended, and this is thus a viable option for an "Onen," who is still obligated in Misvot until the end of Shabbat. (Of course, even if he recites Habdala before sundown, he nevertheless may not perform Melacha until Shabbat ends at nightfall Saturday night.)
If the person did not recite Habdala before sundown, then he may recite Habdala on Sunday after the burial, when he becomes once again obligated in Misvot. He recites the usual Habdala (though without Besamim and "Boreh Me’oreh Ha’esh") even if he ate in the interim. Since he was exempt from the obligation of Habdala, it was permissible for him to eat after Shabbat, and he thus did not any violate Halacha by eating in the interim. As such, he did not forfeit the opportunity to recite a usual Habdala on Sunday.
Summary: One may not eat after Shabbat until he recites Habdala. One who did not recite Habdala on Mosa’eh Shabbat may recite it on Sunday, but without the Berachot of Besamim and Ha’esh. If he ate at some point after Shabbat before reciting Habdala on Sunday, then he recites the Beracha of Ha’mabdil without the phrase, "Hashem Elokenu Melech Ha’olam." He then recites the Beracha over wine and drinks. Somebody who lost a family member during Shabbat, Heaven forbid, should recite Habdala late Shabbat afternoon (after Pelah Ha’minha), before sundown. Otherwise, he recites Habdala after the burial on Sunday, and he may eat and drink in the interim.
