Praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
There are eight categories of people who are eligible to receive Zakah. This is based on the verse in which Allah the Almighty Said (What means): "Alms are for the poor and the needy, and those employed to administer the (funds); for those whose hearts have been (recently) reconciled (to Truth); for those in bondage and in debt; in the cause of God; and for the wayfarer: (thus is it) ordained by God, and God is full of knowledge and wisdom." {At-Tawbah, 60}.
Moreover, Ziyad Ibn al-Harith As-Suda'i narrated: "I came to the Messenger of Allah (PBUH) and swore allegiance to him, and after telling a long story, he said: "Then a man came to him and said: "Give me some of the sadaqah (alms)." The Messenger of Allah (PBUH) said: "Allah is not pleased with a Prophet's or anyone else's decision about sadaqat till He has given a decision about them Himself. He has divided those entitled to them into eight categories, so if you come within those categories, I shall give you what you desire." {Sunna Abi Dawoud}.
The indebted comes within those eight categories, and refers to people overburdened by debts to the extent that they can`t pay them off. Thus, it is permissible to give them from Zakah an amount that suffices for paying off their immediately due debts and covering their basic needs from food, clothing and lodging. This is provided that they had borrowed the money for a lawful matter or else they aren`t allowed to take from Zakah unless they have repented from sin and it was thought most probably that they were sincere in their repentance.
In conclusion, if the debts are already due and the debtor doesn`t have enough money to pay them off, then he is permitted to take from Zakah- as he comes within the category of the indebted-to pay off the rest of the debts. And Allah The Almighty Knows Best.