A brother came to me and Asked "What does he do if his wife told him that she no longer desires to be a muslim....

Praise be to Allaah.

Undoubtedly if this is the case, she has chosen kufr over eemaan. She does not want to stay a Muslim and she is insulting Islam and its symbols... In this case she is a kaafir and an apostate, so it is not permissible for him to stay married to her, because Allaah says (interpretation of the meaning):

"Likewise hold not the disbelieving women as wives" [al-Mumtahanah 60:10]

....If she does not repent then the ruling of Allaah should be carried out on her, which is execution, because the Prophet (peace and blessings of Allaah be upon him) said: "Whoever changes his religion [leaves Islam], execute him."

But if that is not possible and there is no Islamic rule or sharee'ah law in his country, then at least he should separate from her completely; it is not permissible for him to live with her after she has clearly stated her kufr.

Shaykh 'Abd-Allaah ibn Jibreen