What is the ruling regarding a wife's refusal to share her husband's bed if he repeatedly enters into customary marriages (zawaj urfi) and tears up the contract, and does the ruling change if it becomes clear that he marries these women with a guardian (wali) and witnesses, and then separates from them without tearing up the contract?

If a legal marriage contract (with a guardian and witnesses) has been concluded, then the woman is considered the wife of the man. The writing or destruction of the contract does not affect this, whether it is called an 'urfi marriage or not. An 'urfi marriage may refer to a legal but unregistered marriage, or to an illicit relationship that is considered zina (fornication/adultery). The woman must respond to her husband for intimacy, and it is not permissible for her to refuse. If the man is engaging in illicit relationships, she must advise him, and if he does not repent, she has the right to seek divorce due to his transgression.