What is the ruling regarding a married couple who have been estranged for more than seven years, neither of them speaking to the other, living with their children in the same house, and are persistent in their permanent estrangement?

Allah has forbidden turning away from each other and abandonment among Muslims. The longer the abandonment without a legitimate Sharia reason, the greater the sin. And if the turning away and abandonment is between spouses, then that is even more severe. What should be done is for some wise people of religion to mediate between the spouses to reconcile them.