QUESTION: The Beraisa discusses the case of a Na'arah Me'urasah who makes a Neder which her father hears and annuls, but the Arus dies before he hears the Neder. The Na'arah then becomes betrothed a second time on the same day. Her father may annul the Neder together with the second Arus.
The RAN (DH Shama Aviha) explains why this Halachah applies only when the second Erusin occurs on the same day that she made the Neder. When the first Arus dies, the father inherits the Neder because of "Nisroknah." Since the father already heard the Neder, he must annul -- on that day -- the first Arus' portion of the Neder which he inherits from the Arus. If the Na'arah becomes betrothed only on the following day, the Neder is either completely annulled (if the father annulled the Neder on the previous day with the power of Hafarah he received through "Nisroknah") or remains in force (if the father upheld the Neder by the end of the previous day).
The Ran assumes that although the father annulled the Neder before the Arus died, "Nisroknah" still applies. This is the opinion of Beis Shamai as cited by the Beraisa earlier (69a). The Gemara concludes that the Beraisa here, too, follows the view of Beis Shamai. The Ran understands that according to Beis Hillel, however, the second Arus would be able to annul the Neder (with the father) in such a case -- even if the Erusin took place on the following day -- since the father did not inherit the first Arus' portion of the Neder and was not able to annul it or uphold it on the day of the Neder.
However, the Ran himself (69a, DH Aval Beis Hillel) writes that even according to Beis Hillel the father and second Arus may annul the Neder only when the Na'arah becomes engaged on the same day as the first Arus died! According to Beis Hillel, why should the ability to annul the Neder be limited to that day?
ANSWER: The Ran (69a) writes not only that the father and second Arus must annul the Neder on the same day as the first Arus died, he also writes that both the father and Arus must annul the Neder when she gets remarried. Why must the father annul the Neder again? He already did Hafarah on his portion of the Neder while the first Arus was alive! It is clear from the Ran that the Hafarah of the father becomes cancelled at the death of the Arus, according to Beis Hillel. Why, though, should the father's Hafarah be cancelled? The father did not die, and thus his Hafarah should remain intact!
The reason why the father's original Hafarah is void may be understood based on what the Ran writes earlier (67a, DH v'Chazar). If -- at any point after the Arus or father did Hafarah -- there was a time when it was impossible for the other partner to do Hafarah, the Hafarah that was done already becomes void. Similarly, after the Arus dies it is impossible for Hafarah to be done on the second half (the Arus' portion) of the Neder, and therefore even the Hafarah of the father becomes void. This explains why the father must do Hafarah again (with the second Arus) when she becomes remarried. The father's earlier Hafarah became void during the time when there was no one else (i.e. the first Arus) to annul the other half of the Neder.
This also explains why the Hafarah must be done on the same day according to Beis Hillel. The father must do Hafarah again, but his Hafarah is limited to the day on which he first heard the Neder which is the day on which the first Arus died. By the arrival of the following day, he will have lost his right to do Hafarah since the day will no longer be "Yom Sham'o," the day on which he heard the Neder. (Although the father was unable to do Hafarah during the actual day of "Yom Sham'o" and therefore his silence is not considered Hakamah, he still loses the right to do Hafarah, as discussed earlier in Insights to 69:1.)