[Borrowing from a Usurious Bank]

The answer—and Allah is the granter of success: It has been authentically reported from the Prophet—May Allah bless him and his family and grant them peace—[that he pronounced] the curse upon the consumer of usury and the one who pays it. And Allah, Exalted is He, forbade cooperation in sin and aggression, for He said: “And do not cooperate in sin and transgression.” [Al-Mā’idah:2].
On that basis, borrowing from a usurious bank is not permissible in any case, whether the borrowing be for a need or otherwise—except in a case of utmost necessity. “Utmost necessity” is when the necessity reaches the point that a Muslim fears for himself, his children, or his parents death from hunger, or severe cold, or the like, and he finds no way to ward off that necessity except by borrowing from a usurious bank. In that case, it is permissible for him to borrow only what removes that necessity—no more. For it is said: “In necessity, the prohibited becomes permissible,” and Allah said: “… excepting that to which you are compelled.” [Al-Anʿām:119].
Yes—what indicates the prohibition of what we have mentioned is His saying concerning the one who pays usury: “And whatever you give for interest to increase within the wealth of people will not increase with Allah.” [Ar-Rūm:39].
Source: Min Thimār al-ʿIlm wa al-Ḥikmah vol.2