Why would someone insist on staying on when everything seems bad?

There seems to be no love left. Too much damage done. You are hardly even speaking to each other anymore. You have nothing left to offer. You've asked the person to leave you and move out. But he is still there. We are de facto spouses so we don't really need to go through the divorce process. But he refuses to leave, even though he tells me he would real soon. Time has passed and he is still here. He can easily afford to rent an apartment on his income. I don't understand why he is not leaving. Could he possibly be thinking there might still be hope for our relationship? Is he using me for something? I don't do anything for him anymore, besides cooking dinner.