What happens when a 50% owner in a residential home wants to sell and the other doesn't?

When one 50% owner is  a home wishes to sell his or her interest in it, and the other owner does not wish to sell, an impasse results if the person who wishes to keep the owenrship cannot afford to buy out his or her partner in the property.

If that happens, then the result is some partition lawsuit filed in the county courthouse in the county where the property is located where the court orders the property's sale for a certain price and decreases the list price over a period of time if there is not a lot of interest in it.

Typically in the situation that you write about, the one owner who wishes to sell is bought out by the other owner who wishes to keep the property.