All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His Slave and Messenger.
From the words of the husband that he will never divorce her, we understand that she is still his wife. If this is the case, then she is still legitimately his wife, and him being dissolute does not take her outside his marriage bond.
As regards his statement that he will not take her back, if he meant that he will not have sexual intercourse with her as a wife, then he is not permitted to leave her hanging, neither divorced nor married. He has to either keep her in kindness or divorce her in kindness.
However, this man should be admonished and reminded of Allaah, called to repent from those evil deeds, and be advised to have good marital relations with his wife. If he repents and accepts advice, then praise to Allaah, otherwise, it is better for his wife to ask him for divorce even in return for compensation that she pays to him. If he does not accept, she should take her matter to one of the Islamic centers. For more benefit, please refer to Fataawa 225223, 94383 and 92681.
Finally, we would like to point out to the following matters:
1. It is not permissible for a man to have an intimate relationship with a non-Mahram woman, as this is one of the causes of corruption and a means that leads to immorality (fornication or adultery).
2. It is not permissible for a wife to leave the marital home without her husband's permission unless she has a legitimate reason. The fact that her husband is having an affair with that girl does not make it permissible for the wife to leave her husband’s home without his permission.
3. It is not permissible for the husband to abuse his wife by beating and humiliating her; this is an injustice especially if the wife is obedient to him. Allaah says (what means): {But if they obey you [once more], seek no means against them. Indeed, Allaah is ever Exalted and Grand.} [Quran 4:34]
Allaah Knows best.