Now to the married I command, yet not I but the Lord: A wife is not to depart from her husband. 11 But even if she does depart, let her remain unmarried or be reconciled to her husband. And a husband is not to divorce his wife.
12 But to the rest I, not the Lord, say: If any brother has a wife who does not believe, and she is willing to live with him, let him not divorce her. 13 And a woman who has a husband who does not believe, if he is willing to live with her, let her not divorce him. 14 For the unbelieving husband is sanctified by the wife, and the unbelieving wife is sanctified by the husband; otherwise your children would be unclean, but now they are holy. 15 But if the unbeliever departs, let him depart; a brother or a sister is not under bondage in such cases. But God has called us to peace. 16 For how do you know, O wife, whether you will save your husband? Or how do you know, O husband, whether you will save your wife?
— 1 Corinthians 7:10-16.
Paul deals with Christians who, for whatever reason, are married to non-Christians. (This is not a state that a Christian should enter into but may be one in which he or she finds himself or herself after conversion or backsliding.) The apostle uses his authority to say that there should be no divorce, provided that the non-Christian partner is willing to live with the Christian partner. They are regarded as being set apart for each other, and any issue from that marriage is completely legitimate and clean. However, if the unbeliever leaves the believer (possibly the believer’s Christian testimony and lifestyle is something he or she cannot accept), the deserted spouse is not bound to the deserter but is free to remarry. If the unbeliever is willing to stay, Paul argues that the faithful witness of the Christian to the non-Christian spouse may lead to the other one’s conversion. [The Bible Panorama.]