I have a friend who got engaged last year. The wedding was planned for this month. This past spring he and his fiancé bought a house together. Four days after moving into the house, she decided that she didn't want to get married He tried to work things out but she eventually broke things off completely and moved on to a new relationship. They are still living together in the house. Neither one of them can afford the mortgage on their own. My friend wants to sell but she refuses. She wants them to keep living together "as friends". After 7 years together, this feels like a divorce to him and he doesn't want to stay there. He is even considering just walking away and letting the house go into foreclosure. Any advise?

He has to petition the court to force 'partition by sale.'
Laws vary by state. I'm not positive that all states have this, but I think they all do.
He needs to gather all papers and proofs together.
The court will allow her time to buy him out, unless she decides to just agree to this.
He might be able to compromise with her or even pay her the court fee and a little extra to avoid all this and sign an agreement with a real estate broker, if she's a reasonable person and sees that it's unavoidable.

As joypulv indicated, he needs to sue her for "partition". What this amounts to is usually not, as the term suggests, a splitting of the house. In most cases it means to force a sale despite the opposition of the co-owner

Maybe if she sees he is serious about filing suit she will relent and agree to a sale. But ruining his credit by allowing a foreclosure doesn't seem viable.

He may be able and to sell his share. I assume they have their own bedrooms so he could sell his share and stick her with a roommate. He needs to consult a local real estate attorney about this.

...
He may be able and to sell his share. I assume they have their own bedrooms so he could sell his share and stick her with a roommate. ...

It would require permission from the bank (mortgagee), otherwise the due-on-sale clause would be triggered and the bank could foreclose anyway.

Also, he isn't likely to get paid much for an undivided share in a house. Thus it is likely that he wouldn't get cashed out by such a deal. And the buyer probably wouldn't be able to obtain financing, so OP's friend would still be liable on the mortgage.

In short, I don't think this idea would be viable.

It may be a longshot but it is worth pursuing if only the convince the co-owner that he wants out.