I think you hit it when you said he must be leading her on to something and making her false promises. She is getting something out of it to keep staying.
At times I also believe it turns into a win/lose thing for them as well. My exh's OW (see my sitch in Piecing) is still lurking even though I now am 15 weeks pregnant and we are working things out. I do also believe he is keeping her as Plan B just in case or maybe its an ego stroke for him.
Must be a sad and desperate place to be in for them. Getting crumbs here and there....but bottom line is the H's have the power to end it.
Me: 46 FWS: 36 Married and Divorced 4/07, Pregnant 7/07,False R 7/07 Baby Girl born 3/08 Kicked him out because OW: 7/08 5/10 He realized what he had and lost. Moved home! REMARRIED 3/14/11!!