A husband may annul the Nedarim of his wife that are Beino l'Beinah (between him and her). (1)
If an Arusah makes a Neder the right to annul her Neder reverts back to the father if the Chasan did not know about the Neder or if he annulled it before he died.
If the Chasan heard about the Neder and did not respond and he died that day it also reverts back to the father.
If the Chasan heard about the Neder and affirmed it before he died or was silent and he died the next day the Neder may no longer be annulled.
If the father annulled the Neder of his daughter before he died and the Chasan had not yet heard about the Neder the Neder may no longer be annulled. (2)
If the Chasan annulled the Neder of his Arusah before he died and the father had not yet heard about the Neder the father may annul the Neder when he hears about it.
If the Chasan annulled the Neder of his Arusah and the father died before he heard about the Neder the Neder may no longer be annulled. (3)
A BIT MORE
1. He also may annul Nedarim that are Inuy Nefesh (cause physical discomfort).
2. Once the father dies his annulment is Batel and the Chasan may not annul the Neder on his own.
3. Because the Chasan may only annul the Neder of his Arusah with the partnership of the father.
12TH CYCLE DEDICATION
NEDARIM OF A DAUGHTER
Just as a husband may only annul the Nedarim of his wife that are Beino l'Beinah and Inuy Nefesh so too a father may only annul the Nedarim of his daughter that are Beino l'Beinah and Inuy Nefesh. (Ran in the name of the Sifri)
THE DEATH OF THE ARUS
If the Arus dies while the Arusah is still a Na'arah she reverts back to the Reshus of the father. Even if she made Nedarim while she was in the Reshus of the Arus and the Arus heard about it and he died [on that day without annulling the Neder] the father may annul the Neder by himself on the day that he hears about it. (Shulchan Aruch YD 234:11)