What is the ruling if the husband initiates Khul' upon his wife in exchange for an amount equal to half the total dower owed from her debt?

Primary text

The Khul' is valid, and the entire dower obligation is extinguished. Half of the dower is settled by set-off (Muqassah) against the consideration for the Khul' that is in her debt to him, and the other half is cancelled by the divorce itself.