I Corinthians 7

15 But if the unbelieving depart, let him depart. A brother or a sister is not under bondage in such cases: but God hath called us to peace.1
People are subject to their own actions. The unbelieving man or woman married to a Christian can depart at his or her own will even though the Christian does not desire it. However, it is always better for the couple to remain married. Nevertheless, the Christian does not have to go to unnecessary lengths to keep the partner. Notice the “unbelieving” person (apistos) is an “unfaithful” person. Marriage is a bond (Ex. 22, Dt. 22) between two people, and in the case of an unfaithful spouse and a faithful partner, staying on the course of faith is what is important. Hence, a faithful partner is not “under bondage ”/ obligated to keep or disallow the deviate from making a bad choice of separating. Let him or her go.
However, the decision is critical as to remaining single if that is the choice. Abstinence is required (v.11).
Heresies attempting to give validation for various excuses have arisen against the requirement to stay single after divorce cases. Cause is actually insignificant. One I've been questioned with is “abandonment”, which seemingly is just another way of “departing” (v. 15) with or without notice. This act does not give the spouse a right to remarry.
A simple physical and spiritual reason (natural and biblical/spiritual/special agreement revelation) no excuse is valid is that the abandoned spouse's partner still holds a cognizance-factor of the left partner. Until death of the partner, neither would be free to bid for marriage. The female already has a one-male cognizance and the male already has a one-female cognizance. Either mate leaving this sexual pure state and bonding sexually with another would develop a two-person cognizance, a state of impurity. Jesus Christ referred to the example of Adam and Eve as to marriage, each having a one-partner cognizance. They were pure. Thus, abiding single after divorce is the only way to stay pure and not increase the cognizance factor to impurity.
Remember, The Apostle Paul started the chapter recommending celibacy (v.1). To avoid impurity (fornication: v.2), he recommended marriage (a pure state of bond and institution implemented by Adam and Eve). Following an initial, pure wedding ceremony will prevent sexual immorality.

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1The Holy Bible: King James Version. (1995). (electronic ed. of the 1769 edition of the 1611 Authorized Version., 1 Co 7:15). Bellingham WA: Logos Research Systems, Inc.