They kind of give up if they have gone to the bottom of he pecking order. It is kind of like they are in a depression about not having any friends.
I have a turkey in one of the chicken houses because the other turkeys were picking on her and making her bleed. She pouted like that for several days but has snapped out of it. Interestingly enough she stopped growing and is the same size as the hens - half of the size of the other turkeys.
I'm worried about the extreme lethargy. If she is that far down she may be a goner. It's possible that she has coccidiosis as well. I'd watch them and if you seen signs in the others start medicating the water.
The only live chicks I will bring on this farm come in the mail at a day old. They are just too touchy. The first sign of sickness is usually death.