We currently have the "married house" on the market,
So, if its on the market, then he still has ownership of the house along with her, so unless its stated in the divorce that she has sole possesion of the property till its sold, he has as much right to the house as she. In other words, unless he is forbidden to access to the home, he HAS access to the house.
If she is awarded the house, then either it's paid for and she needs to get a quit claim deed to remove him from the home ownership paperwork (and it will protect him from lawsuits that may arise from injuries sustained on that property), or it's not paid for and he has to keep making the mortgage payment for some reason (like, he makes way more money)-- good luck getting him to give up a sense of ownership in that case.
Or it's not paid off and she has to refinance the house in her name only -- meaning he gets half the equity in the house, and then she still needs to do a quit claim deed to remove his name from the deed to the home.
What she needs to do is set him up on a date with a distant friend to get him to worry less about her and more about his own life.