Have you checked really closely to be sure she doesn't have something caught around her neck like a string or something. I have had them look something like that when they have stuck their neck through a fence wire / chicken wire trying to get away from something and got stuck or had a hard time trying to pull it back out.
Is there run just dirt and no grass but there is grass growing on the other side of the fence just within their reach? If so I would think this is from the fence because they are trying to reach grass.
Maybe a little free ranging could be arranged with you watching them if there is a risk of predators.
It does look to me like a got-stuck-in-the-fence type of line. But it could have something do do with molting, especially if the separation is where the neck feathers turn into body feathers... you get a line something like that when they raise their hackles, it is just a lot more pronounced than I usually see.