Is the husband's wealth, on which he does not pay zakat, considered unlawful, and is it permissible for the wife to partake of it, and how can his wealth be purified from the zakat he missed?

Zakat (definition) is a fundamental pillar of Islam, and there is a severe warning against withholding it. You should advise your husband and remind him of the gravity of preventing zakat, seeking help from Allah and from those who have influence over him. Not all of his money is unlawful, and there is no harm in living with him. For repentance, he must pay zakat for all previous years during which he did not pay zakat.