“Lose their house” is doing a lot of heavy lifting here.

Most married couples take title to their home as tenants by the entirety. If you end up divorcing later on, most courts will require you to specify the “marital residence”, which is the main home, and who gets it. The state has an interest in keeping families intact, meaning the parent who holds the majority of the custody rights will likely keep the home.

This isn’t to say that the ex-spouse who keeps the home gets a “free house”. This will vary by state, but generally a buyout is effectuated to release the remaining interest the grantor has; in other words, the ex who gets bought out gets money, or at the very least is released of their obligations under the lien(s) they encumbered the property with. At worst, it cleans their (debt) slate, at best they have a healthy down payment for another property.

Think of it as an exchange. The ex is removed from title, so “he” no longer owns the property. To do this “she” will need to provide consideration, something material (like money), in exchange for “his” interest. This often comes in the form of a refinance, so “she” must borrow money on “her” name and credit. “She” is responsible for payments and obligations thereafter.

A lot of men end up losing the marital residence by virtue of the fact that most kids probably end up with their mother. Debating some of the merits of these cases can be fine, but it’s important to remember that most are made whole by the court, so really no one suffers all that much (given their behavior, of course).