I know this sort of example. My mate was basically that ex, and he'd always go on about his ex girlfriend and her new boyfriend, and how much he hates him. He'd keep in contact with his ex constantly, and meeting up every so often. I always thought my mate was being a dick for this, and his ex even worse, because it seems she just wants both relationships.
If this was happening to me I'd want to confront her about it, and chances are it'd be a breakup. Either she cuts the ex go, or you can find a better girlfriend.