Is it permissible for one who has taken out a riba-based loan to receive zakaah in order to pay off his debt?

Firstly: 

We
ask Allah, may He be exalted, to forgive you and pardon you for what you
have done, for riba is a major sin, concerning which there are warnings such
as have not been issued with regard to other sins. Allah, may He be exalted,
says (interpretation of the meaning):

“O you who believe! Fear Allah and give up what remains (due
to you) from Ribaa (from now onward) if you are (really) believers.

279. And if you do not do it, then take a notice of war from
Allah and His Messenger”

[al-Baqarah 2:278-279]. 

It
was narrated that Jaabir (may Allah be pleased with him) said: The Messenger
of Allah (peace and blessings of Allah be upon him) cursed the one who
consumes riba and the one who pays it, the one who writes it down and the
two who witness it, and he said: they are all the same.

Narrated by Muslim (1598). 

For more information on the warning to the one who deals in riba, please see
the answers to questions no. 60185 and
141948. 

Secondly: 

If
you have repented from this riba-based transaction and have resolved not to
do it again, and you regret having done it, but it is not possible to avoid
paying this interest because the system obliges you to repay loans with
interest, then there is no reason why your relative should not help you to
pay off this debt, and there is no sin on him in doing so, because that
comes under the heading of relieving your distress. The Prophet (blessings
and peace of Allah be upon him) said: “Whoever relieves a Muslim of
distress, Allah will relieve him of distress on the Day of Resurrection.”
Narrated by al-Bukhaari (2442) and Muslim (2580). Moreover, the longer your
repayment of the debt is delayed, the more the interest that you owe will
accumulate. As for helping one who has repented to pay off debt, there is
nothing wrong with that, and it does not come under the heading of helping
in committing evil in any way whatsoever, so the one who wants to help may
give some of his zakaah to the debtor, if the latter does not have wealth
surplus to his needs with which to pay off his debt. 

The scholars have stated that if one who got into debt for a haraam purpose
has repented to Allah, there is nothing wrong with giving him zakaah funds 
with which to pay off his debt. 

Shaykh
Muhammad ibn ‘Uthaymeen (may Allah have mercy on him) said: 

Question: if a person gets into debt for a haraam purpose, can we give him
zakaah?

Answer: if he has repented, we may give him (zakaah funds), otherwise we may
not, because in that case it is helping in something haraam. In that case,
if we give him he will go into debt again.

End quote from ash-Sharh al-Mumti‘ (6/235) 

Dr. ‘Umar Sulaymaan al-Ashqar said: If a person takes out a riba-based loan,
it is not permissible to pay off his debt from zakaah funds aimed at helping
debtors, unless he repents from having dealt in riba.

End quote from Abhaath an-Nadwah al-Khaamisah li Qadaayaa az-Zakaah al-Mu‘aasirah
(p. 210) 

And Allah knows best.