The Bible is clear that marriage has been from the beginning, intended to be between one man and one woman, for life. God made woman as a help meet for man. It is something I struggled to reconcile with as well. I Corinthians 7 is the most common passage people will turn to (or be taught by someone) in order to justify divorce and remarriage. Paul is making it clear that it his opinion he is giving (and NOT from the Lord), regarding not being under bondage, but peace for us regarding the unbelieving spouse departing. There is no mention of being free to remarry in I Corinthians 7. This would contradict what Jesus taught in Matthew 5, 19 (see also Mark 10 and Luke 16). Paul also speaks on this in Romans 7.
Now some will point out that the passages in Matthew 5 & 19 give an exception for fornication. This is yet another reason to look into why some zealots like myself adhere to the King James Bible, for being based on the Textus Receptus, not the Sinaiticus & Vaticanus. I'm speaking of the books like ESV, NIV and the rest. The ESV uses "sexual immorality" in place of fornication, where the NIV just uses adultery. So why does the King James use term fornication? There is a difference - one is done within a marriage and the other is outside of marriage.
The book of Matthew addresses a mostly Hebrew audience that would have been more familiar with the Mosaic law. Under mosaic law, you didn't divorce your adulterous wife, but rather she was to be put to death. Fornication however, was something that involved sexual activity before marriage. That was the exception Jesus was speaking of. See Deuteronomy 22 & 24. Paul, having been once a Pharisee would have had been well schooled in the Mosaic law. And no we are not still under the law, and Jesus was not contradicting the law. He says in that same part of Matthew 5, that He came not to destroy the law, but to fulfill.
The passage in Matthew 19 is where the pharisees are tempting Jesus into contradicting the law or Moses regarding divorce. He puts them to silence and merely reminds them that from the beginning that God's original plan was for one man and one woman - for life. This is yet another reason that we, as believers need to be very careful who we choose for a spouse. In Judges chapter 11, a man named Jephthah makes a vow to the Lord he regrets, but has to adhere to it.
So the options for someone whose spouse might or has left them
(1) try to stay with them or reconcile the marriage
(2) remain unmarried until the departing spouse dies
