I was in a relationship like that once - I really felt second best for ages with my fella's ex ringing him for advice (her life was going pear-shaped after the split) and texting and stuff. He never lied about the contact or anything like that but I kept my distance, emotionally, because I could see that it was unfinished business in his mind. They weren't angling to get back together but he was still bitter and wanting answers as to why she had finished it.
We got on well so we maintained the relationship we had - no real commitment on anyone's part, as much as I wanted it to change. It came to a head one day when I noticed him reading a text and I saw "meet you" in it - it was from her. I just asked him to be honest with himself about what he wanted and whether I was part of that equation - then I left.
I think because we had been together several months at that point he suddenly realised what he had to lose - a fresh start. Or he could spend the rest of his life waiting for someone who couldn't make her own mind up.
Is he worth the wait? That's what someone asked me.