How old is your hen and how long has she been laying? I've seen one of those incomplete eggs before, my hen passed it after getting a very big fright. Quite often the causes of odd eggs are stress-related and I suspect that may be the case here. You can read more about odd eggs and causes here:
She is older. Not exactly sure. I got the whole flock from a lady nearby. She said coyotes were getting them, so she wanted to get rid of the whole flock. I've had them for three+ weeks now, and I've only gotten four eggs. After the third day they have been free ranging every day. They have two feed stations and access to clean water. The few eggs I did get had a very thin shell.
Awww, I bet with some more patience and love they will settle right into the new home you've provided and start laying for you. Sweet girls. Mine do this occasionally and I don't find rhyme nor reason to it. I get a random rubber egg, then other days get shells so hard and thick I can hardly crack 'em.