Question:

If two people are divorced for unbiblical grounds and there is no adultery at the time, yet one spouse after the divorce marries someone else or is sexually immoral is the other then free  to remarry another?

Answer:

"And I say to you, whoever divorces his wife, except for sexual immorality, and marries another, commits adultery; and whoever marries her who is divorced commits adultery" (Matthew 19:9).

The allowance for remarriage comes from the exception cause. A person who divorces and remarries, in general, commits adultery. That is because, despite the divorce, the person is still bound by the terms of the marriage covenant that he made.

The exception clause implies that if the divorce was because of sexual immorality then the person not guilty of the sexual immorality can remarry without being guilty of adultery.

Therefore, since the divorce was not because of fornication, then the general rule applies -- to marry again is to commit adultery. Both parties are still bound by the terms of the covenant they originally made. Just because they divorced it does not imply that God has released them from their oaths.

"So He said to them, "Whoever divorces his wife and marries another commits adultery against her. And if a woman divorces her husband and marries another, she commits adultery"" (Mark 10:11-12).

I am not sure you answered my question. Maybe my question was not understood. 

Two people get divorced not for fornication. One is waiting and praying for restoration. The other decides to marry someone else or get sexually involved with another. Are you saying that now the faithful spouse who has been hoping for restoration is never free to remarry in this situation? Is this what you believe to be the truth?

If a marriage is ended because of fornication then the spouse who stayed true to his or her marriage vows is free to remarry in the Lord?  

A marriage ended for unbiblical reasons and after the divorce one partner becomes an adulterer and marries another. Now faithful spouse is never free to marry as long as her former spouse is living (but would have been if the fornication took place before the marriage ended?)

It appears you understand what Jesus stated quite well. You just don't want to accept it. That is something I can't help you with. Just because you do not like an answer, it does not imply that your question was misunderstood. If you want to argue otherwise, you will have to show where God supports your position. Emotional charged questions won't make a matter right or wrong.

All vows are serious matters. And the vows made before the Lord are even more serious (Ecclesiastes 5:2, 4-5). Marriages are founded upon a covenant, which involves God (Malachi 2:14; Matthew 19:6). Therefore, only God can set the rules as to when parties who enter a covenant may be released.

If a person decides to end his marriage, not because his spouse broke the terms of their marriage covenant through fornication, then he did so knowing he has only two options open to him. "Now to the married I command, yet not I but the Lord: A wife is not to depart from her husband. 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" (I Corinthians 7:10-11). Since they are unmarried, as Paul stated, sexual sins by the other spouse does not change reason the marriage ended. One cannot divorce a person to whom they are not married.

I accept the wisdom of God placing this severe condition on leaving a spouse. God hates divorce (Malachi 2:16); thus, He made the consequence of divorce severe. If people submitted to God's will, divorce would once again be rare in this world.