A question that can come up when students first learn that heathens in historical times had divorce and that the wife was the key holder in most times in heathen history (with some notable exceptions) is: what happened after that? If the woman was the property owner did the man lose his status after divorce?
That's a good question, and the answer is sometimes, but not usually. Social status in the ancient world depended on a lot more besides being landed or not. A man would only lose status when he left his wife's property if the man's status was tied to the estate, which was not always the case. That had to do with how much property was involved in the marriage, which was more an issue with the upper classes, and whether there were any noble titles involved, also only an issue for the upper classes, and only in some time periods.
An example would be if the property on which they lived were exclusively her inheritance and getting divorced meant he had to stop being a land holding lord and go join some other lord's house carls. But that would have been a really small percentage of people. It would not affect most people.