Is it obligatory to fulfill a vow to slaughter an animal for a specific person every year, knowing that the animal is expensive, that the affection for that person has ceased, and that fulfilling the vow might lead to a problem with the future husband?

It is not permissible for a woman to be in a romantic relationship with a man who is a stranger to her. And this vow, being in disobedience, does not necessitate fulfillment. What is obligatory is an expiation for breaking an oath, based on the Prophet's (peace be upon him) saying: "There is no vow in disobedience, and its expiation is the expiation of an oath."