Masechet Kinim deals with the resolution of mixtures of bird offerings. Much like animal offerings, birds offering can either be obligatory or voluntary. An obligatory "ken" consists of two birds, one chatat (sin offering) and one olah. The Mishnah teaches that if a woman offered the chatat and then died, the heirs would still be required to bring the olah. If however she had offered only the olah, then the heirs could not bring the chatat. We shall try to understand this law.
The Rosh cites the Gemara (Kidushin 13b) where there is a debate regarding this Mishnah between Rav and Shmuel. One holds that the heirs are only obligated to bring the remaining olah if it had already been set aside while the woman was still alive. The other opinion however holds that even if it were not separated, the heirs would bring an olah. This is because the obligation is written in the Torah and is therefore equivalent to a contractual loan that can be collected after the borrower has died. There is consequently a lien on the woman's property for the fulfilment of that "loan". The Tosfot Yom Tov, citing the Rambam, explains that we rule like the latter opinion.
From the wording of the Mishnah it seems that the family are only obligated to bring the olah if the chatat had been offered. This is indeed the opinion of the Rashbatz who explains that if the chatat had not been offered then the obligation to bring a chatat disappears with her death, and consequently the obligation to bring an olah as well.
The Ramban explains similarly. Firstly. the olah should not be offered before the chatat. More importantly, the Ramban maintains that the obligation to bring the olah only begins after the chatat is offered. He cites the Mishnah from Negaim (14:11) that discusses the korban oleh ve'yored, as proof. Recall that for those korbanot, that which is offered, be it bird or beast, depends on the financial standing of the individual. The Mishnah there teaches that if one's financial position changes in the middle of offering the korbanot (e.g. they inheritted a large estate) it is their position at the time that they offered the chatat that determines which korban must be offered.
The Tifferet Yisrael however argues that even if the chatat was not offered, the family would still be obligated to bring the olah. He cites the Gemara (Pesachim 59a) that the precedence of the chatat is a mitzvah, and offering the birds out of order does not invalidate the korban. Indeed, the Ramban cites the Raavad, that it is even if the chatat was designated but not yet offered, the family would still bring the olah, since at the time of separation it already fixes the type from which birds must be offered. The Tifferet Yisrael explains that the wording of the Mishnah, that suggests that the chatat has already been offered should be understood in the context of the law just described; that is that both birds must be from the same type -- turtledove or young pigeon. In other words, if she offered the chatat then died, despite her death, the family must still bring the olah from the same type.
Perhaps this debate can be understood in the context of the discussion of how to understand the ken, the pair of birds, in general. The achronim discuss whether we understand the two birds as independent offerings despite one necessitating the other. Alternatively, it can be understood that they are considered one korban despite consisting of two birds that are offered in very different ways.
Perhaps that Raavad maintains the first understanding, that as long as the birds have been designated, despite the fact that the chatat cannot be offered, there is no issue with offering the olah. One can then suggest that the Ramban maintains the latter understanding, such that if the chatat has not been offered, the entire "single" korban cannot be offered, so it cannot help by offering "half" of it, the olah, alone.1
1 This latter understanding can perhaps help us understand how the olah can be offered at all after death, despite the chatat being offered. Normally, obligatory offerings cannot be offered after death. If however we understand that the chatat and olah are considered one offering, since part of the korban has already been offered, when can the perhaps understand why this case is different.
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