If a person who is liable to pay zakat becomes poor before giving their zakat and dies, is their zakat obligation…

If a person who did not pay their zakat on time later becomes poor and dies without settling their zakat debt, they are not absolved of the zakat obligation. Such a person should instruct their heirs to pay the zakat debt on their behalf. If they die without making such a will, they are considered sinful. If the heirs pay the zakat on their behalf, it is hoped that the deceased will be freed from this debt.

If, after zakat becomes obligatory on a property, it is lost involuntarily through theft, loss, or seizure—regardless of whether the owner is able to pay or not—the Hanafi school holds that the zakat obligation is lifted. If the property no longer exists, zakat is not required. According to other jurists, however, the zakat obligation continues and the person must pay it. However, it is unanimously agreed that zakat must be paid on property that has been disposed of through donation or sale. (See Ibn Abidin, Radd al-Muhtar, 2/266; Bilmen, Ilmihal, 321-322)

Source: T.C. Diyanet İşleri Başkanlığı, Din İşleri Yüksek Kurulu