What is the Shar'i ruling on a wife remaining in limbo after her husband abandoned her and divorced her verbally without completing the divorce procedures, knowing that he is an alcoholic and does not wish to end this marriage?

A husband abandoning his wife is an act of injustice and sin. If he divorces her and her 'iddah (waiting period) expires, he has no way to return to her except through a new marriage contract. It is not permissible for her to accept his return as long as he remains in the same state.

However, if the 'iddah is still ongoing, he has the right to take her back. She should, nevertheless, request a divorce from him due to his iniquity and the harm inflicted upon her. If he refuses, she has the right to refer the matter to a Sharia judge to remove the harm.