All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
This person should turn to Allaah, the Exalted, in repentance and pay that money back to its owner. If he cannot do that, then he should give it to another patient who is in need of money. The basic principle in this regard is the generality of the Hadeeth that reads, "Due upon the hand to take care of what it took, until it is returned." [At-Tirmithi] The Prophet, sallallaahu ‘alayhi wa sallam, also said: “What I have ordered you [to do], do as much of it as you can…” [Al-Bukhari and Muslim]
Moreover, it is incumbent on this person to fulfill his vow. Allaah, the Exalted, highlighted the characteristics of the residents of Paradise, saying (what means): {They [are those who] fulfill [their] vows and fear a Day whose evil will be widespread.} [Quran 76:7] The Prophet, sallallaahu ‘alayhi wa sallam, said: "Whoever vowed to obey Allaah, the Exalted, must obey Him; and whoever vowed to disobey Allaah, the Exalted, must not do so." [Al-Bukhari]
If he cannot clear his liability from that money, which was entrusted to him in order to give it to that patient, and fulfill his vow, then he should give precedence to repaying the money that he owes over fulfilling his vow. This is because the rights due to Allaah are potentially subject to His forgiveness, whereas a right due to a human must be fulfilled, unless he relinquishes it. One should give precedence to repaying what he owes and fulfilling people's (financial) rights over fulfilling the Rights of Allaah, the Exalted, such as vows and expiations, if he fails to fulfill both at the same time. The mercy and grace of Allaah, the Exalted, are immense. He is the All-Rich and Praiseworthy. He is the Most-Forgiving of creditors, and the Most Generous of those who are generous. Indeed, He graciously and generously pardons the debtors. He may pardon His slaves for not fulfilling His rights with or without their repentance. However, one's liability for people's rights is never cleared except by fulfilling them or seeking those people's forgiveness and pardon.
This is the opinion adopted by Al-Azhar's Fatwa Committee, as it has stated the following:
If a person is liable to two financial rights; one to Allaah, the Exalted, and the second to people, and he cannot fulfill them both at the same time, then it is incumbent on him to give precedence to fulfilling people's rights over the Rights of Allaah, the Exalted. When the person is indebted and he, before repaying his debt, makes a vow to build a mosque or give some money in charity but he does not have enough money to repay the debt and fulfill his vow, then he should repay the debt first. Afterwards, he should fulfill his vow whenever he can afford it, after repaying all his debts and clearing his liability of all financial rights that are due to other people. If he could not afford to fulfill his vow after it became due, then he should seek forgiveness from Allaah, the Exalted. He is All-Forgiving and All-Merciful; His mercy and forgiveness are vast.
Allaah Knows best.