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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...

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...