He could be sick or injured, even if pooping normally.
Sometimes an animal will bully another because it's sick, or something's not right with it, or sometimes the animal will end up being sick or having something not right with it because of the bully, and the bully either way makes an issue out of something which isn't necessarily an issue in the first place, if you follow me.
Some birds are psychologically more delicate and will almost give up on life if bullied. Sometimes a bird will just remain in one area all day every day to avoid bullying.
This may not actually be because it's a weaker bird, as per the common belief, but because a chance issue like a broken bone has rendered it unable to defend itself. A decent kick to the ribcage by the bully could easily break a few ribs and render the other one unwilling to fight back any longer.
I would separate the aggressive one for a few days to see if the other one starts acting normally, but that runs the risk of the bully not being able to be reintroduced for the sake of the others, since separating them resets their pecking order and they have to sort it out all over again. If you want to keep the bully, separate the injured bird instead, but whichever one you separate, you may have issues reintroducing it.
Even if the unwell one does act normally minus the bully, you will likely be forced to choose between the two and rehome or kill one. If he acts normal without the bully, you know it's the bully being an issue, but if you then release the bully, that one will need to battle to reestablish his hierarchy level and your unwell bird will most likely be first in the firing line.
The only permanent fix is to get rid of the bully in most cases.
I don't keep birds that bully sick or injured birds because otherwise you end up with a flock that kills members for something equivalent to a broken toe or small cut wound, easily healed issues which instead are costing you much time and effort and costing birds their lives.
They are bullies due to individual character, it's not something they are all naturally prone to at all, just like cannibalism and chick-killing and so forth --- they are not something all chickens will automatically do in a given circumstance, contrary to some textbooks' claims. In fact scientific studies done recently on poultry found they are one of the few animals capable of learning and exhibiting compassion; they're nowhere near as unintelligent as we're taught they are.
I've never had a problem with violence with mine because I culled bullies out so only peaceful birds bred on, and I highly recommend not breeding bullies no matter the excuses one can rationalize their behavior by, it's just more lives wasted down the track.
Best wishes.
