Coop/run is all open.....being in TX maybe and open air type coop/run?they free range half my backyard...about a 15x60 foot fenced area. and their coop/run is a 6x12 6ft tall enclosure so I don't think they are crowded...
they have completely stripped the yard so is it boredom? they have constant access to feed and water.
the trouble maker is a Barred Rock and her sidekick is an Americana. The victim is one of two Leghorns.
My RIR, Astralorp and Welsumer don't pick on her at all.
Or is there a smaller, enclosed coop portion to your setup?
The one picked on being injured, could be the basis...they can drum out the weak...and separation, then reintroduction, of injured bird can make it worse.