Alms Tax: Priority of Zakat, Khums, Hajj, and Debt from the Estate of the Deceased
Practical Laws of Islam as per the teachings of Ayatullah Sistani
Ruling 2001
If a person owes khums or zakat, and ḥajjat al‑islām[1] is obligatory for him, and he has debt as well, then, if he dies and his estate is not sufficient for all of these obligations, in the event that the wealth on which khums and zakat is obligatory has not perished, the khums and zakat must be paid and the rest of his estate must be used to settle his debt. However, if the property on which khums and zakat is obligatory has perished, his estate must be used to settle his debt. If after this anything is left, it must be spent for [hiring someone to perform] hajj [on the deceased’s behalf]; and if after this anything remains, it must be divided between the khums and zakat debts.
-Ayatullah Sistani, Practical Laws of Islam, Alms Tax (Zakat)
Ḥajjat al‑islām is the term used for the hajj that is obligatory for a Muslim to perform once in his lifetime, as opposed to a hajj that is obligatory for a Muslim by means of a vow and suchlike.