The braisa (Daf Yomi: Nazir 25b - 26a) states: Other people who are obligated to bring bird offerings by the Torah (because they cannot afford to buy animal offerings) who already designated the money to buy the birds (and then became rich), if they now want to bring a chatas or olah offering instead, they may do so.
The Mefaresh understands this Gemora to be referring to a rich woman who has given birth, where her chatas is a bird.
It is noteworthy that after the Torah discusses the korban that a rich woman who has given birth brings, it says [Vayikra 12:7]: This is the law of a woman who gives birth to a male or to a female. The question is asked: Immediately following this verse, the Torah teaches us the korbanos that a poor woman who has given birth brings. Why would the Torah say regarding the rich woman’s korbanos that “this is law of a woman who gives birth”? It would seem from the verse that only the rich woman’s korbanos are the law, and not the korbanos from the poor woman.
The Kli Chemdah (Parshas Tazria) cites a Gemora in Menochos (110a): It is written: This is the law of an olah. The Gemora expounds: Anyone that studies the laws of an olah is considered as if he brought a korban olah. What would be if a poor person would recite the portion dealing with the rich person’s korbanos? Would it be regarded as if he brought the korban? The answer may be gleaned from the fact that the Torah concluded the portion dealing with the rich woman’s korbanos with the following verse: This is the law of a woman who gives birth. The Torah is informing us that the recital of this portion is sufficient for anyone, even for a poor woman.
[The Gemora states that Hashem told Avraham Avinu that whenever Klal Yisroel will read the Torah portions pertaining to the korbanos, it will be regarded as if they brought korbanos and their sins will be forgiven.
The commentators discuss if this concept applies by other mitzvos as well. Perhaps it can be said that the studying of any mitzvah that cannot be performed nowadays will be regarded as if one fulfilled the mitzvah.
The Chafetz Chaim cites the Gemora in Bava Metzia (114b) that the Amoraim were fluent in Seder Kodoshim in the same manner as Seder Moed, Nashim and Nezikin. This is because Kodoshim was relevant to them since the learning about the korbanos was regarded as if they actually brought a korban. Implicit in his words that for some reason this was only true regarding Seder Kodoshim and not to Seder Zeroim or Taharos which also has many halachos that do not apply outside of Eretz Yisroel and after the destruction of the Beis Hamikdosh.
The Taz in his sefer Divrei Dovid maintains that the concept applies to all mitzvos and one who studies the laws of Zeraim, it will be regarded as if he gave terumos and ma’asros to the kohanim and levi’im and it will be considered as if he gave all the presents to the poor people. This is the explanation in Yaakov’s words to Esav "Im Lavan garti," which Chazal understand to mean that Yaakov kept all 613 mitzvos in Lavan’s house. There were many mitzvos that he was not able to fulfill at that time; it is evident that the studying of these mitzvos are regarded as if he fulfilled them all.
The Ben Ish Cahi explains the verse in Nitzavim: "Ki Korov eilecha hadavar meod b’ficha u’vilvov’cha la’asoso." It is possible to fulfill all the mitzvos with your mouth (by studying them) even those mitzvos that you cannot actually perform.]
We can add that the Mishna in Negaim compliments this explanation. For the Mishna says that if a poor person who is a metzora brings the korban that a rich person is supposed to bring, he fulfills his obligation. The Chinuch (123) states by a korban olah v’yoreid - (certain sins which require a korban chatos, he either brings an animal, bird or flour offering depending on his status - this is called a fluctuating korban) if a poor person brings the korban of a rich person, he does not fulfill his obligation. The Chinuch explains the reason: the Torah had compassion on the poor person, it is not proper for him to compel himself to bring a korban which he cannot afford. How can the Chinuch hold against the Mishna, which explicitly states that he does fulfill his obligation?
The Chasam Sofer answers based on the following Gemora in Shabbos: Hashem punishes each person according to what he can afford. A rich person who sins will lose his cow. A poor person, on the other hand, will lose his chicken or some eggs. Therefore, there is a distinction between the korban of a metzora or a woman who gave birth and the korban olah v’yoreid. A metzora is not required to bring a korban because he sinned, it is to purify him and allow him to eat kodoshim. If a poor metzora decides to bring the rich man’s korban, he will have discharged his obligation. Conversely, a sinner who does that will not have discharged his obligation, for here the Torah prescribed for him the korban which will give him atonement according to his status. The korban is in place of the punishment. It is not decided by the pauper what his punishment should be, and therefore when he brings the korban of a rich person, he does not fulfill his obligation.
The Sfas Emes (here and quoted in Moadim U’zmanim as a story which occurred by a Kenesiya Gedola) answers that there is a basic distinction. A metzora disregarding if he is rich or poor, is required to bring a chatas and an olah. The rich man brings animals and the pauper brings birds. If a poor person brings the korban of a rich person, he fulfills his obligation, for he brought the prescribed amount. A korban olah v’yoreid is different. A rich person brings an animal for a korban chatas and a poor person brings two birds, one for a chatas and one for an olah. If a poor person will force himself to bring the korban of a rich person, he will not fulfill his obligation because he cheated the Altar out of one korban - namely the olah.
There are two questions on this explanation (look in Shemuas Chaim and in Mitzvas Hamelech from Harav Ezriel Cziment). Firstly, the Chinuch says a different reason for his not fulfilling his obligation. He says because the Torah doesn’t want a poor person to overburden himself. He does not say the reason of the Sfas Emes that he missed a korban? Secondly, one must ask, why is it that a poor person is required to bring two korbanos and a rich person only brings one? The Ibn Ezra explains the reason for this: A chatas bird is completely eaten and an olah bird is completely burned on the Altar. These two birds together replace a regular korban which entails a human consumption and the Altar’s consumption. They are actually one korban. Therefore, one can say that a poor person is not missing a korban by bringing one animal instead of two birds?
It would seem, however, that this question can be answered. Even according to the Ibn Ezra, the two birds are not one korban. They are two korbanos complimenting one another. The rationale behind bringing the two korbanos could be because the Torah wants human consumption and the Altar’s consumption; nevertheless, it is still two korbanos and a poor person is missing one korban when he brings the korban of a rich person.
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