What is the ruling on a vow in which my relative vowed to pray until she committed to prayer, but she was unable to commit to it and stopped praying, and what is its expiation?

The one who abandons prayer enters Saqar (Hell), and the Prophet, peace and blessings be upon him, said: "Between a man and polytheism and disbelief is the abandonment of prayer." Therefore, your relative must fear Allah and pray, as prayer is obligatory upon her whether she vowed to pray or not. Allah the Almighty has indeed warned those who neglect prayer. She must repent to Allah before her time runs out, and vowing to perform the obligatory prayer is vowing to do what is already obligatory by the fundamental ruling of Islamic law.