What is the ruling regarding a husband divorcing his wife when he denies it, and what is the ruling regarding his failure to provide for her?

Divorce is not established except by the husband's admission or by lawful evidence. If the husband denies that a divorce occurred and the wife has no evidence, his word is accepted.

If the wife is certain that the husband uttered an explicit divorce, and this divorce completes the three pronouncements, then it is not permissible for her to remain with him, and she must seek khul' from him.

Regarding maintenance: The husband is obligated to provide maintenance for his wife as long as the marriage exists and she is not disobedient (nashiz). If he does not provide for her, she has the right to refer the matter to the judiciary to compel him to provide maintenance or to separate them. She also has the option to annul the marriage if the husband becomes unable to provide her maintenance.