She can file for divorce by herself. That gets the process started. Eventually they will serve me with the papers. And eventually the judge will grant her divorce even if I object. That is the whole point of "no-fault" divorce. She doesn't have to prove I did anything wrong to divorce me. She just has to keep saying "I no longer want to be married to him" often enough over a long enough period of time, and the judge will grant her request even if I prefer to remain married to her.

As for the house, doesn't matter whose name is on the deed. It is marital property. It will be divided up as part of the divorce. If the judge gives her the house, she gets the house.

Now, that is oversimplified and there can be details that would make it more or less likely depending on the facts of a particular case. But in this case. Where we bought the house while we were married. With down payment funds that came from a joint account. And have been paying the mortgage with money I earned during the marriage. Then the house will almost certainly be seen as marital property subject to equitable distribution. Even though only my name is on the deed (done not to prevent her from owning a share of the home, but to hide her from the guy who was stalking her at the time we bought this house). And even though the down payment on our first house came entirely from money I earned before we got married, and that was more money than we put down on this house.