Is the husband responsible for his wife who requested khulʿ but did not complete it, and did not contact him, knowing that he left her content?

Khul' (divorce at the instance of the wife) does not take place merely by saying, "Go and divorce yourself through khul'"; rather, it requires an offer and acceptance from both parties in exchange for a compensation. If the offer and acceptance are completed, or if a judge rules it, then the wife becomes irrevocably divorced (ba'inah) and cannot return to her husband except with a new marriage contract. However, if this does not occur, the wife remains under the husband's marital bond, and he is obligated to treat her kindly by providing maintenance, housing, and chastity. He is responsible for her, as Allah Almighty says: "Men are in charge of women by [right of] what Allah has given one over the other and what they spend [for maintenance] from their wealth." He is also obligated to spend nights with her, though scholars differ on its duration. Some hold that it is not obligatory, others that it is obligatory one night out of every four nights, and still others believe that no specific duration is set and it is left to ijtihad (independent reasoning). If the woman waives her right to maintenance, housing, or spending nights, there is no sin.