1) ONE WHO FINDS OUT THAT HE IS OBLIGATED TO BRING A KORBAN CHATAS ON THE DAY BEFORE YOM KIPPUR
The verse states that the Sa'ir ha'Na'aseh bi'Fnim, the goat offered by the Kohen Gadol on Yom Kippur, the blood of which is sprinkled in the Kodesh ha'Kodashim, atones for the "impurities of the Jewish people, and from their Pesha'im (intentional sins) for all of their Chata'os (unintentional sins)" (Vayikra 16:16).
The Gemara (7b) quotes a Beraisa which derives from the words "Pesha'im" and "Chata'os" that a Chet can be compared to a Pesha. Just as no Korban is brought for a Pesha (since no Korban is brought to atone for a deliberate sin, with the exception of Shifchah Charufah), the Chata'im for which the Sa'ir atones are those for which no Korban is brought.
The Gemara (end of 8a) suggests that this excludes a case in which the person knew that he became Tamei but forgot and entered the Beis ha'Mikdash or ate Kodshim, and afterwards he realized his sin. The Gemara asks that no verse should be necessary to teach that this case is excluded from the atonement of the Sa'ir ha'Na'aseh bi'Fnim. Since the person must bring a Korban Chatas Oleh v'Yored for his sin, it is not logical that the Sa'ir ha'Na'aseh bi'Fnim should atone for it.
The Gemara answers that the verse is necessary for a case in which the person only found out shortly before sunset on Erev Yom Kippur that he had eaten Kodshim while he was Tamei. RASHI (DH Samuch) explains that one might think that because he did not have sufficient time to bring the Korban before Yom Kippur, he indeed is exempt when the Sa'ir ha'Na'aseh bi'Fnim is brought on Yom Kippur. The verse therefore teaches that even in such a case the Sa'ir ha'Na'aseh bi'Fnim does not atone for his sin.
Why is it necessary for the Gemara to say that he found out about his sin shortly before the onset of Yom Kippur? Even if he would have found out on the morning of Erev Yom Kippur, he still would not have been able to bring a Korban, because of the principle stated by the Gemara in Pesachim (13b): one may not offer a Korban when it will not be able to be eaten for the allotted number of days, and the meat will likely end up as Nosar. (This rule is known as "Ein Mevi'in Kodshim l'Beis ha'Pesul.")
Since a Korban Chatas may be eaten for one day and one night (see Zevachim 53a), it follows that one may not bring a Korban Chatas on the morning before Yom Kippur because he thereby will lose the opportunity to eat the Chatas at night. (This is the reason why "Mizmor l'Sodah" is omitted from Pesukei d'Zimrah in the morning service of Erev Yom Kippur. That chapter of Tehilim corresponds to the offering of a Korban Todah, which cannot be offered on Yom Kippur since it cannot be eaten on Yom Kippur night. See REMA OC 604:2.)
Accordingly, why does the Gemara say that the person found out about his sin shortly before sunset? Even if he discovers his sin much earlier, on the morning of Erev Yom Kippur, he still is not permitted to bring his Korban Chatas before Yom Kippur.
(a) The PORAS YOSEF suggests that since Rebbi Shimon is mentioned in the Beraisa, it may be that he is consistent with his opinion in Zevachim (76a), where he disagrees with the law of "Ein Mevi'in Kodshim l'Beis ha'Pesul."
1. However, the Poras Yosef questions this answer. The Gemara in Zevachim implies that Rebbi Shimon is lenient only b'Di'eved, but not l'Chatchilah. The Gemara suggests that Rebbi Shimon allows bringing Korbanos in such a case only when the purpose is "l'Tikunei Gavra" -- "to make a person fit" to bring Korbanos if his status will be changed by the Korban (such as in the case of a Metzora).
(b) Therefore, the Poras Yosef suggests that the principle of "Ein Mevi'in Kodshim l'Beis ha'Pesul" is only mid'Rabanan, but mid'Oraisa one may bring a Chatas on Erev Yom Kippur. Since the Gemara here is explaining the verses of the Torah, the Gemara mentions a case in which the person finds out about his sin only shortly before sunset. If he would find out about it in the morning, he would be able to bring his Korban on Erev Yom Kippur, mid'Oraisa.
Similarly, the MELECHES BETZALEL cites the SHA'AR HA'MELECH (Hilchos Pesulei ha'Mukdashin 6:18) who also writes that the principle of "Ein Mevi'in Kodshim l'Beis ha'Pesul" is only mid'Rabanan. The Sha'ar ha'Melech cites TOSFOS in Pesachim (89a, DH Hani) who also implies that the reason for this law is that the Korban might become Nosar, which is only a concern only mid'Rabanan.
(c) The Meleches Betzalel suggests another answer to the question. The Gemara here indeed may follow the view of Rebbi Shimon, as suggested by the Poras Yosef. The Poras Yosef's question on his answer is not difficult. Perhaps the purpose of bringing the Korban on Erev Yom Kippur is indeed "l'Tikunei Gavra." As mentioned earlier, Rebbi Shimon agrees that the prohibition of bringing Kodshim to the Beis ha'Pesul does not apply in such a case. The Meleches Betzalel explains that the reason why this is considered "l'Tikunei Gavra" is that the purpose for bringing the Chatas is to protect the person from suffering (see Rashi to 8b, DH Nisli). As long as he does not bring his Korban, he is in danger of Divine punishment. Therefore, there is no greater form of "l'Tikunei Gavra" than this. (D. BLOOM)
2) MAY ONE OF THE TWO "SE'IRIM" OF YOM KIPPUR BE OFFERED WITHOUT THE OTHER ONE?
QUESTION: The Mishnah (2a) states that the "Sa'ir ha'Na'aseh bi'Fnim" together with Yom Kippur suspends atonement for people who originally knew that they had become impure, and later forgot about their Tum'ah when they entered the Beis ha'Mikdash or ate Kodshim. Later, when they realize their sin, they will bring a Korban Chatas Oleh v'Yored.
If, however, the person did not know originally that he had become Tamei, but he later realized that when he entered the Beis ha'Mikdash or ate Kodshim that he was in a state of Tum'ah, the "Sa'ir ha'Na'aseh ba'Chutz" together with Yom Kippur atones for his sin.
The Gemara here asks that since the two Se'irim are compared to each other (as the Gemara earlier teaches), why does the Sa'ir ha'Na'aseh bi'Fnim not provide atonement for both situations? It should atone not only for a person who knew originally that he had become Tamei and later forgot, but also for a person who did not know originally but found out later.
The Gemara explains that this would be significant if the Sa'ir ha'Na'aseh ba'Chutz was not offered. RASHI (DH Hachi Garsinan v'Nafka) writes that this might occur if they did not have enough goats.
The Gemara here seems to contradict the Mishnah in Menachos (27a) which states that the two goats of Yom Kippur are "Me'akvin Zeh Es Zeh" -- "they hold each other back." This means that both of them must be offered, or neither of them may be offered. Why does the Gemara discuss a situation in which only one of them might be brought?
(a) The MITZPEH EISAN answers that only when there are two goats may one not be offered without the other. However, if only one is available, the absence of the other does not prevent the first one from being offered. (The Mitzpeh Eisan cites a proof for the notion that "Me'akvin" applies only when sufficient Korbanos are available from TOSFOS in Menachos (45a, DH u'Minayin).)
(b) The RASHASH, CHAZON ISH (OC 127:14), and others also understand that when only one goat is available, it may be offered. However, they maintain that in such a case the Sa'ir ha'Na'aseh ba'Chutz should be offered, and not the Sa'ir ha'Na'aseh bi'Fnim. This is implied by various Gemaras, such as the Gemara in Yoma (62b), which states that in order to designate a goat as the Sa'ir ha'Na'aseh bi'Fnim, a lottery between it and another goat (which will be offered as the Sa'ir la'Azazel) is required.
However, they note that this is inconsistent with Tosfos' conclusion (DH l'Tum'ah), based on the Gemara here, that in such a case the Sa'ir ha'Na'aseh bi'Fnim would be offered. Tosfos makes a simple deduction: the Gemara asks that since the Sa'ir ha'Na'aseh ba'Chutz should atone both for the sin for which it is brought, and for the sin for which the Sa'ir ha'Na'aseh bi'Fnim is brought, what is the practical difference if both are brought anyway? The Gemara does not answer that the difference would be in a case in which only the Sa'ir ha'Na'aseh ba'Chutz is brought. This clearly implies that if there would be only one goat, only the Sa'ir ha'Na'aseh bi'Fnim would be brought. The Chazon Ish asks, therefore, what is the reason behind the Gemara's implication that if there would be only one goat, the Sa'ir ha'Na'aseh bi'Fnim would be brought?
The Chazon Ish writes that Tosfos apparently rules like the Gemara in Yoma (62b), which implies that the Sa'ir ha'Na'aseh ba'Chutz would not be valid if offered before the regular Korbanos of the day, because it would be deemed as being brought "before its time." Indeed, the RAMBAM (Hilchos Yom ha'Kipurim 5:3) writes that that if the ram or goat of the Korban Musaf was offered before the daily service of Yom Kippur, it is invalid. The source for this ruling, the Chazon Ish asserts, is the Gemara here. Just as a Chatas Chitzonah is invalid if offered "before its time," that is, before other Korbanos that are supposed to be offered first, so, too, the ram or goat of Musaf is invalid if it is offered before the Korbanos that are supposed to precede it. The Chazon Ish therefore suggests that the Gemara in Yoma is the source for the words of Tosfos here. (It also seems that according to Tosfos the lottery is not "Me'akev" the offering of the Sa'ir ha'Na'aseh bi'Fnim, and it is required only l'Chatchilah.)
(See also CHIDUSHEI HA'GRIZ HA'LEVI on the Rambam, in the name of his father, RAV CHAIM SOLOVEITCHIK.) (D. BLOOM)