What is the ruling on a husband leaving his wife in a state of suspension, neither divorced nor provided for, and does the husband incur sin for this, especially if the wife is the cause of the dispute and refuses divorce?

A wife has the right to a suitable, independent dwelling provided by her husband. If she waives this right and agrees to stay with his family, there is no harm in it. It is not permissible for her to leave without her husband's permission if he provides for her. However, if he neglects her and does not provide for her, she may leave to seek her livelihood. Her leaving her family's home without her husband's permission is wrong, but it does not invalidate her right to maintenance. He must provide for her and secure an independent dwelling for her. If her staying alone entails harm, she should be prevented from doing so.