Even though that may seem to be a solution to their problem, it is not the right thing to do according to the Bible. To understand why, let us first consider what a Declaration Pledging Faithfulness is and when it may be used.

The Declaration Pledging Faithfulness is a document signed before witnesses by a couple who cannot get married legally for the reason explained in the following paragraphs. When they sign this document, they promise before God and human witnesses to be faithful to each other and to legalize their marriage if that becomes possible. The congregation then views the couple’s marriage the same as if they were in a legalized marriage.

When is the Declaration Pledging Faithfulness used? To answer that, we first need to understand how Jehovah views marriage and divorce. Jehovah made human marriage and views it as very serious. His Son said: “What God has yoked together let no man put apart.” (Matthew 19:5, 6; Genesis 2:22-24) He added: “Whoever divorces his wife, except on the ground of fornication, and marries another commits adultery.” (Matthew 19:9) So “fornication,” or sexual immorality, is the only reason mentioned in the Bible to end a marriage. If, for example, a man has sex with someone who is not his wife, the wife can decide whether she wants to divorce him or not. If she chooses to divorce him, then she is free to marry someone else.

Especially in the past, the main religion in some countries did not accept what the Bible says about divorce. Instead, it taught that divorce is always wrong. Religious leaders had so much power that the law in some countries today does not allow people to divorce, even for the reason mentioned by Jesus. In other countries, the law allows for divorce, but it is extremely difficult and complicated to get one. It might take many, many years. The main religion or the government in these places stops people from doing something that God allows them to do.​—Acts 11:17.

For example, a couple may live in a country where it is impossible or extremely difficult to get a divorce. If they have done everything possible to end a previous marriage and, according to the Bible, are free to marry again,  they may sign the Declaration Pledging Faithfulness. It is for countries like these that Jehovah’s organization lovingly prepared this document. It is not a document to be used in countries where divorce is possible, even if it is a bit expensive or complicated to get.

Some who live where divorce is possible have wanted to sign the Declaration Pledging Faithfulness and, in this way, avoid the trouble involved in getting a divorce. But that is not the right reason to use this document.

Let us go back to the situation described in the question. The man and woman are living together and want to marry. Neither of them is married to anyone else. According to the Bible, they are both free to marry. This is not a situation in which either of them needs a divorce and cannot get one because of the law of the country. So the Declaration Pledging Faithfulness cannot be used by this couple. The problem in their case is that the man is not in the country legally, and because of that, the government will not allow the marriage. (In many countries the authorities will allow a marriage even if the man or the woman or both of them are living in the country illegally.) So, what can this couple do? They might have to go to another country where they can legally get married. Or it may even be possible for them to get married in the country they live in if the man does what is needed to become a legal resident.

So the couple can make the changes needed to obey both God’s laws and those of Caesar. (Mark 12:17; Romans 13:1) If they get legally married, they may be in a position to get baptized.​—Hebrews 13:4.