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Hi this is Dr. Hill. Please give me a moment to type my full response. Thank you.
It sounds like she has a reproductive issue. When they egg is laid without a shel or a very thin or soft shell, this is typically a sign of quick transit through the reproductive tract and associated with metritis. Have you made any changes in husbandry over the last few weeks? What diet are you feeding? Any supplements? Does she free range? Was she vaccinated for Mareks as a day old chick? lets start there.
Also, are any of the other hens having abnormal eggs?
So, I would stop their access to the dog and cat food. It is not healthy for them. That may be your issue. Is she having normal stools?