I have heard of women going 46-48 weeks, but I would think it's extremely unusual! I don't know that there's a useby on the placenta, as such, but that once it starts to go that's a signal for labour to begin.
It's possible dates are wrong. It's also possible that a woman tests positive, miscarries, but doesn't know it, and then conceives again. Though, again, it would be extremely unusual to lose a baby and have no indication of that.