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, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
If the oath-taker died before paying the expiation for breaking his oath, it should be paid from his estate before distributing it among the heirs. The Shaafi‘i scholar Shaykh Zakariyya Al-Ansaari said in his book Asna Al-Mataalib, "If a free person passed away before paying the expiation for breaking his oath, the expiation is considered a debt owed by that person to Allaah The Exalted and a right of Him. Thus, fulfilling this right should be given precedence over the rights of human beings. It should be paid before distributing the inheritance among the heirs, whether he mentioned it in his will of not. This is based on the Hadeeth where the Prophet, sallallaahu ‘alayhi wa sallam, said: 'The debt due to Allaah The Exalted is the one which most deserves to be paid.'"
The Maaliki scholar Muhammad ‘Ulaysh said in his book Fat-h Al-Jaleel, when he highlighted some of the rights related to the estate of the deceased, "Then, the rights of other human beings over the deceased should be settled, such as debts that have been authenticated by evidence or by his acknowledgment of them, whether in his illness or in the state of health before someone who cannot be accused of fabricating the whole story (about the debt). Then, the rights of Allaah The Exalted – such as Zakah, expiations, and vows – should be settled."
It was mentioned in Al-Fataawa Al-Hindiyyah, according to the Hanafi school of Fiqh, "Whoever passed away or was killed and did not pay the expiation for breaking an oath, it should still be paid."
Allaah Knows best.