Must the wife repay the bank loan taken out by her deceased husband, given that she had asked him to take out the loan to help her children and had agreed with him to repay her share of it, and is the debt of the loan religiously waived for her because the state is non-Muslim?

Borrowing and lending with usury is a grave sin for which Allah has promised the direst consequences to its perpetrator. The Prophet, peace and blessings be upon him, cursed the one who consumes usury, the one who feeds it, its scribe, and its two witnesses. One must repent to Allah; for whoever repents, Allah accepts his repentance.

Regarding the repayment of the loan, if you pledged to your husband to repay the entire loan, then you must repay it all. If you pledged to repay only the part you took, then you must repay that part. If the husband leaves behind assets, his debt must be paid from them before fulfilling any bequests and distributing the inheritance. Only the principal amount of the loan should be repaid, without the interest, for Allah Almighty says: "And if you repent, then you will have your principal sums. You do not wrong, and you are not wronged." If it is possible to avoid paying the interest, then that is obligatory; otherwise, it must be paid. The presence of the bank in a non-Muslim country does not exempt one from repaying the loan, because a Muslim is required to fulfill his obligations unless they are forbidden.