The Injured Fellow is one of the many inhabitants of the sanctuary, Topple Town. He is specifically found at the Red Ogre Inn, inside Topple Town. Judging by the fellow's title, it is clear that he has injured his head by or with something. This may be referencing to the 'silly dispute' that the Ancient Warrior was implying about while visiting the inn.
Players can interact with the Injured Fellow, gaining access to one piece of dialogue. Here is the dialogue:
"I've hurt my head, so I'm resting at the inn."
It is clear that the Injured Fellow had hurt his head by or with something or someone and that he's resting in the inn to heal his head overtime.