The marriage and divorces certificates provided by government officials are a side show and have no status in God’s economy.
Human governments do not have authority over marriage. They cannot change something that God has established, so Christians should not allow them to define marriage for them. God has already defined marriage and human governments cannot change God's word. Christian marriage should be based on God's word and not on legislation established by a human government.
When unbelievers get married, God is the witness to their marriage, not the state (Mal 2:14). Their commitment to each other and their consummation of that commitment is what makes their marriage. Isaac was married to Rebecca when he accepted her as her wife and “took her into his tent” (Gen 24:69). He did not have a marriage certificate from the state, but he was married in God’s eyes.
In the same way, when a husband commits adultery, or persistently assaults his wife, she is no longer bound to him in God’s eyes. It is irrelevant whether the divorce papers have gone through or not.
If a woman who is deserted by an unbelieving husband meets another man and commits to him, and cohabits with him, she is already married to him in God’s eyes. It does not matter, if the state has recognised the divorce or if they are legally married again.
Getting other believers and elders who know the situation to support the person’s understanding of God’s witness will be important to avoid making rash mistakes. Agreement of two or three will be important.
Once a woman or man has left and begun a marriage with a new partner (in God’s eyes) his preference is that they should not go back to a previous spouse (Jer 3:1).