Divorce, as common as it is, is an ugly and devastating turn of events in someone's life. In studies about stress and life happiness, divorce is consistently rated as one of the most prominent indicators for stress and unhappiness in life. It could ruin someone's social circle, their family structure, and put them in financial ruin. Because it's so devastating, it's common for people to do anything and everything in their power to keep their marriage, even in the face of something as shocking as infidelity.
Some people don't work for it though. Some people are satisfied with giving up, not fighting for their marriage, and moving on. If you're someone on this route, well it's your life and you can do what you want. But at least do the right thing, meaning to file for a proper divorce, go through with all the proceedings, paperwork, asset separations, and financial implications. Refusing to move out is a whole other realm of weird…