Alms Tax: Zakat and Debts of a Deceased Person
Practical Laws of Islam as per the teachings of Ayatullah Sistani
Ruling 1909
With regard to someone who has a debt and possesses the actual property on which zakat has become obligatory, if he dies, the entire zakat must be given from the property on which zakat has become obligatory, and then the debt must be repaid. However, if he is liable to pay a debt of zakat [as opposed to his actual property having become liable for zakat], then this debt is like his other debts.[1]
-Ayatullah Sistani, Practical Laws of Islam, Alms Tax (Zakat)
This means that if the combined total of his zakat debt and his other debts is equal to or less than his estate, his zakat debt and his other debts must be repaid. However, if the combined total of his zakat debt and his other debts is more than his estate, his estate must be proportionally divided between those entitled to receive zakat and his creditors.