What should one do who vowed to sacrifice a whole, half, or quarter animal if so-and-so dies, then repented and came to love her while she is still alive, and fears dying before fulfilling his vow?

If a person conditions their vow on the death of someone, for example, by saying: "If so-and-so dies, I will slaughter (an animal)," then fulfilling it becomes obligatory upon that person's death, because a vow conditioned on a stipulation becomes binding when the stipulation is fulfilled. It is important to note that conditioning a vow on someone's death might be understood as wishing for the death of a Muslim, which is reprehensible, unless the deceased was known for their oppression and wickedness.

Ibn Qasim Al-Abbadi stated: "If he said, 'If I am blessed with a child, or if I return safely from my journey, or if so-and-so dies, or if I find such-and-such, then I have bequeathed one-third of my wealth,' this is permissible, and the condition should be acted upon. I say: This is a vow in meaning, so one should consider his statement: 'or if so-and-so dies,' and similar phrases, in terms of the good intention behind it and otherwise."

Sheikh Ibn Baz was asked about vowing to fast upon the death of an oppressor, and he replied: "Vowing is forbidden and disliked; it should not be done. The Prophet, peace and blessings be upon him, said: '(Do not make vows, for vows do not avert anything from the decree of Allah, and they only extract from the miser).' However, if one vows an act of obedience that is lawful, they must fulfill it, based on the Prophet's saying, peace and blessings be upon him: '(Whoever vows to obey Allah, let him obey Him; and whoever vows to disobey Allah, let him not disobey Him).' So, whoever vows an act of obedience from among the acts of worship, such as recitation, charity, or prayer, on a suspended condition, then if the condition is met, they must fulfill it."

Therefore, you are obligated to fulfill what you vowed if that woman dies before you. However, if you die before her, there is no obligation upon you due to the cessation of responsibility.