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.

Most of a man's social status would revolve around his birth family, foster family if applicable, his deeds, his profession, and favor with social superiors. Most of a woman's social status would revolve around the same things, but one must understand that housewife was an actual occupation considered to be a "real job" in the context of heathen cultures so her accomplishments in that career counted toward her status. If a Viking Age housewife were making a modern style resume it might include things like "managed 12 permanent staff plus up to 20 seasonal workers" or "established a new horse breeding operation" or suchlike.

There were times and places in heathen history where the upper classes didn't actually own any property at all, except for the king. The king distributed lands along with noble titles. This concentration of social and economic power in one man's hands was one of the driving forces of the colonization of new lands, to provide economic opportunities. Each time heathen people established a new colony they reverted the the model of property ownership in which individual households owned and managed lands and homes, with the housewife keyholder as the owner and manager. The power of kings was left behind. Iceland had no king at all, but was founded as a democracy, which it remains.

In the times and places in which the king granted lands along with titles, there was a system of military alliance between the kings and the lesser nobles under the king, so that the lands a noble couple managed flowed not from her inheritance but from his vassalship under a king. The rise of liege lord relationships and vassalship occurred in the wake of the breakup of Charlemagne's Holy Roman Empire, and so, coincided with the age of conversion to Christianity, which did not yet allow divorce. Even while pagan subjects were leaving mainland Europe to colonize new lands, such as Iceland and Greenland along with various islands, and establish new heathen countries throughout the Viking Age, the kings and upper nobles of Europe had converted to Christianity by then. Iceland remained heathen longer than mainland Europe. So the question of what would happen after divorce in the countries in which the lands of nobles were grants from the king rather than individually owned was a moot point as divorce was no longer practiced then.

People who didn't hold land or noble titles as a result of marriage did not have any of their personal status tied up in the marriage so divorce would not have affected their status. The vast majority of people living in ancient times did not have noble titles.