The question arises that if a Christian spouse walks out of a marriage with another Christian, does the one who breaks the marriage contract cease being a believer in the view of the church? In the 1st Century, walking out of the family home, which we call separation today, was seen as divorce.
If we look at the Matthew reference where Jesus spoke of a believer who sinned not accepting correction at the different levels and ultimately not listening to the church, being then treated as a tax collector and an infidel. In other words, according the church the person becomes a non-believer, and that no one in the church should fellowship with that person. The idea was to show the sinner the consquences and to encourage the person to repent and be restored to fellowship. Repentance in terms of divorce would have been a reconciliation between the two.
If we now look at 1 Corinthians 7:15, we see that if an unbeliever wants to leave the marriage to a Christian believer, the believer should let the unbeliever go (ie: divorce the believer) and the believer would be in no bondage to the marriage. Without referring to the Matthew passage the definition would be that that unbeliever would be a non-convert. But taking the Matthew reference into account, then in the view of the church, a person walking out of a Christian marriage and refusing to take correction, would be an unbeliever, and therefore the person left behind would be in no bondage to the marriage and be quite free to remarry without penalty from the church or from God.
Furthermore, 2 John 9 says this: " Anyone who runs ahead and does not continue in the teaching of Christ does not have God; whoever continues in the teaching has both the Father and the Son." This means that if a professing believer does not continue in the teaching of Christ, he does not have God. In other words, he is not a true believer. Therefore, if a professing Christian walks out of a marriage, or has to leave because of adultery or domestic violence, then he is no longer a believer and can be treated as such. In fact, the believing spouse, according to 2 John, should not have the person in the house or eat a meal with them. The only way that such a person can repent is to be reconciled to the innocent spouse. If he or she refuses, then the innocent spouse is free to remarry without any penalty.
This is an instance where Scripture interprets Scripture and settles the question of whether an innocent spouse in a divorce can remarry.