if you were running off with someone else would you take the engagement ring? or if you were going to hurl yourself into an abandoned construction pit? this is what makes me think that she had something to do with it.
If she were simply running (not "running off") she might very well have taken off her rings because the hands swell. Mine do. I also take off my rings when cooking messy meals, clearing brush, and doing something with rubber gloves (like painting), because my diamond sometimes pokes through. Because my darling husband bought me some serious bling-bling and my rock is larger than average, I also don't take my engagment ring when traveling to Third World countries or going places where my sparkly rock might attract undue attention (oops, does that make me a racist?). So the fact that she left her ring behind when going out for a jog at night shouldn't be the sole indicator in determining that she may have run away.