you can save the relationship as long as he is willing to do the same. He will have to break it off with the other person. Hopefully, she knows that the two of you are still living together.
He may be acting this way because he believes that you'd be there for him no matter what. But, the fact remains - he's dating someone at the same time. Figure out what led to the break up after such a long time together, what he wants out of you and what is he going to do with the other person. Let him know that you're not replaceable and that if he does not do something about this, you may not be there waiting for him.