This may be a long shot, but I have to ask....is she acting broody? While the green can be from feed, grass, or illness, it also looks very similar to broody poo. Her behavior also sounds like she is brooding in a corner. Some hens will poo in their nesting spot, and it will coat on their behind. A brooding hen will be fixated on a particular spot, many without eggs under them, puffed, and grumpy at anyone or any thing that comes around them. They will sit fixed and staring into space like a trance. When you pick them up they will rouse, but want to immediately return to that spot they've chosen for brooding...which is why I ask since many sick birds will "hunker down" wherever they are placed as they don't feel well while a brooding hen will return to her brooding spot.
I've had hens go broody at all times of the year. I've hatched numerous chicks under a broody hen in the dead of winter.
However, if she looks sick...then obviously this would be a sign of her illness.
LofMc