The Short Answer
Yes. The Quran explicitly identifies “the debt-ridden” as the Sixth of the Eight Categories of people entitled to Zakat (see Surat Al-Tawbah, 9:60).
What Are Its Stipulations
Legal scholars specify differing conditions that qualify one’s debts for Zakat payment. This leads to variant rulings about who counts as debt-ridden. Yet by any measure, this category of eligibility for debt-relief in Islam remains without parallel in our times or any preceding time.
In brief:
The Hanafis permit Zakat payment of debts for anyone who has debts they cannot meet and whose wealth falls below the threshold for paying Zakat (nisab).
Malikis, Shafi’is, and Hanbalis distinguish one’s Zakat eligibilty for debt payment based on two different causes of one’s debt accrual.
Personal reasons
In the service of communal or civic duties done for the good of society
What Is the Zakat Payment Threshold?
Not all wealth is Zakatable. Different kinds of Zakatable wealth have their own minimum thresholds, called nisab, literally origin,’ or ‘beginning,’ so called because the right of the poor in a Muslim’s Zakatable wealth commences at the point where one’s wealth reaches nisab after a lunar year (hawl) passes on it. Wealth fluctuations above nisab over the course of the year do not matter for the three schools. Fluctuations of Zakatable wealth below nisab, once it is reached, have no impact on the ruling of the Hanafis, as long as nisab is there at the beginning of the Zakat year and on its due date. The Hanafi position on nisab is the relevant one in the case of determining one’s eligibilty for debt payment by Zakat for those following this school of Law because this ruling requires that one’s Zakatable wealth be below nisab.
Here is a table of nisab values on various types of wealth.