If you spam-squeeze chickens next to the edge of your chicken stick boundary they can get embedded in the invisible wall boundary. You can still interact with them, but they are un-moving. Someone else has reported that incubating eggs in stuck chickens does not allow you to get the baby animal back (I suspect as the chicken is unable to approach you to "give" you the new animal.)
I have not yet tried removing the chicken stick to see if this will free them, wanting to preserve the bugged state for the moment. There are two of my 3 chickens in my new /home exhibiting this behavior.
See also: http://www.glitch.com/forum/general/17389/