Our hens were hatched in March and came to live with us in July. The 4 of them were all laying by the middle of September. They've been faithfully laying 1 egg each day. Last week, we found an egg w/o a shell ruptured under the perch. There was about 2 more times that we found eggs w/o shells. We know the eggs of one of our hens but not all 4. 3 days ago, we started getting just 3/ day. About 10 days ago we moved the run & coop to the winter location--under a pine tree and over the cement patio. About that time, I noticed some gray clumps and streaks near the vent of our biggest and earliest maturing hen (Big Red). She doesn't perch, she lays on the cover of the nesting boxes so my hubby wondered if that was a carry over mess. My hubby also started adding antibiotics to their water. I mentioned to my husband that we needed to do something to help manage the pooh on the patio and we have since remedied this. tonight, Big Red was not herself. I reviewed the signs of illness section of the BYC4 Dummies book and started trying to figure out what made the most sense. She is the most talkative and I didn't hear a peep from her, she followed the others around but didn't participate, she didn't come running when I threw some feed on the sidewalk--all things she normally does. The only animation I saw was when she was fighting over a mouse with another hen (this is a new experience for us--they killed it but didn't draw blood nor eat the mouse). She went into the coop while the others were eating the sidewalk feed. When I went to bring more water to the coop, she was already laying down but she saw the water and jumped down to drink. I noticed the egg and membrane. On the food & roosting side of the coop, there was a wet, clear mess mixed in with the bedding. Once having a drink, she started to eat and has been eating for the past 30+ minutes. Have you seen anything like what's in the picture before? Did she have egg binding? The egg was normal size but was partially coated in a white chalky substance (didn't rub off), there was a dark spot on the egg (looked similar to a scab). The way it was on the shelf is pretty accurate for how it wound up in one of the food bowls when I moved it. Advice?