It is permissible to give Zakat to a person who is wealthy but is also in debt, specifically to pay off that debt. This is based on the clear text of the Qur'an.

Allah, the Most High, has specified the recipients of Zakat, saying: "Zakah expenditures are only for the poor and for the needy... and for those in debt..." ([Surah At-Tawbah 9:60](/quran/9/60))

Shaykh Ibn 'Uthaymeen explained that 'those in debt' (al-gharimin) are one of the eight categories eligible for Zakat. He clarified that debtors are of two types:

1. A person who incurred debt to reconcile between others. This person is to be given Zakat to pay off that debt, even if he is wealthy, as an encouragement for such noble deeds.

2. A person who incurred debt for his own permissible needs (such as for housing, medical treatment, or marriage) and is unable to pay it off.

Regarding the second type, if a person possesses wealth (e.g., property, assets) but this wealth is not liquid or is essential for their living (like their primary residence), and they are unable to pay a due debt, they may be given Zakat. The Zakat given should be equivalent to the amount needed to clear the debt.

However, if the person has sufficient, accessible wealth from which they could pay the debt, they are not eligible to receive Zakat for this purpose. The zakat is intended to relieve the burden of the debt itself. Therefore, a person who is otherwise well-off can be a recipient of Zakat, but only in the amount that will settle their outstanding debt which they cannot pay from their own available funds.