The king was the highest authority within the Walls and he was noted for his continued support of the Survey Corps despite the popular opinion against them. In reality however he was just a symbolic figure with no true authority and a puppet king, servant of House Reiss, who acted as a substitute for the true king Rod Reiss.
This unnamed old man was careless, apathetic, lazy and possibly alcoholic. His only concerns are petty things such as eating. He seems pretty unconcerned about the critical situation and the ongoing deaths. The true powers ruling over humanity were a much larger conspiracy and the Survey Corps were a threat to their shady business. It's unknown what happened to him after the arrest of the noble rulers and his removal.