Is it permissible for a wife to take money from her husband without his knowledge to pay off her debts that he refuses to settle, despite his abundance of wealth?

The husband is not obligated to pay his wife's debt unless it is a voluntary act on his part. If the husband spends on his wife and children in a reasonable manner, the wife is not permitted to take anything from his money without his permission. This is because she is entrusted with his money and is responsible for it, based on the Prophet's (peace be upon him) saying: "The woman is a guardian in her husband's house and is responsible for her guardianship," and his saying: "A woman should not spend anything from her husband's house except with his permission."