I have a case of this in my family tree and it threw me for ages.
With the help of people from Rootschat I was able to determine that the 'Widow' had been left by her husband. The husband had bigamously married another women and had children with her. I'm descended from his second family.
In my case what seems to have caused the split is his adultery and abuse. People on Rootschat pointed me to some newspaper articles which stated that he was once arrested for assaulting her. She was also taken to court for attempting suicide as a result of his abuse.
I'll never know, but I suspect that she knew he was still alive but that she agreed to say he was dead to anyone in authority in exchange for the pleasure of never seeing him again!