Husband and Wife have a fight. It is the culmination of many such fights. In a rage, Husband packs his bags and leaves home. He never returns.
Husband is a reservist in the army. A war breaks out and he is called up to serve. He is sent abroad, never to return.
Husband is the captain of a ship. He leaves home for a long journey at sea. Wife does not join him. The ship sinks and nobody aboard survives.
Husband goes on a business trip abroad. Wife stays at home. Husband does not return when he is scheduled to. Nobody hears from him again.
Husband and Wife are separated during the Holocaust. Wife survives but is unable to locate Husband.
Years pass. Wife gets on with her life. She meets a man who proposes marriage to her. She wants to accept, but may she?
The answer to that question, if she is a traditional Jew who wishes to abide by the halakhah is no. According to the halakhah, Wife is still a married woman. If she remarries without unequivocally ascertaining Husband's death, she will have committed adultery, an act which is absolutely prohibited by Jewish law.