Is it permissible for a woman to use all means of birth control—including tubal ligation—given that she has a daughter suffering from health problems requiring constant care, and she had become pregnant and miscarried?

The tubal ligation for sterilization is Islamically forbidden except in cases of extreme necessity, such as when pregnancy poses a danger to the mother's life, or causes her illnesses she cannot endure, or if no other contraceptive method is available. In these cases, the procedure is permissible, and there is no blame upon her.