Praise be to Allaah.
It is haraam to take out a riba-based loan to buy a house or
anything else. You did well to refuse to do that and advise your parents
accordingly.
The one who takes out a riba-based loan should pay back the
original money, but he is not obliged to pay the interest unless he is
compelled to do so. It is permitted for him to use trickery to avoid it.
Based on that, if your father’s aim in filling out this form
is to reduce the debt or interest, then there is nothing wrong with it and
there is nothing wrong with your filling out the form. But if the aim is to
get involved in more riba, or to extend the loan period with an increase in
interest, in this case it is an interest-based transaction, and it is not
permissible for you to help your father with this transaction, because
Allah, may He be exalted, says (interpretation of the meaning):
“Help you one another in Al‑Birr and At‑Taqwa (virtue,
righteousness and piety); but do not help one another in sin and
transgression. And fear Allaah. Verily, Allaah is Severe in punishment”
[al-Maa’idah 5:2].
But if not submitting this application will result in him
going to jail, in that case it is permissible for him to submit it because
it is a case of necessity, and it is permissible for you to help him with
it.
See also the answer to question no.
99149
And Allah knows best.