Ellis and Ruckly are two Chronics. The Chief mentions them as the mistakes of the system, and as examples of the terrible things done to the inmates of the mental institutions. They are examples, too, of how the institution threatens the inmates with the shock therapy.
Nurse Ratched operates by intimidation. Ruckly and Ellis are examples of two Acutes whose treatments have gone poorly, so the Acutes do not want to act up and be sent to electroshock therapy. The Chief describes Ellis and Ruckly in Chapter Three:
The staff, now, they consider Ruckly one of their failures, but I’m not sure but what he’s better off than if the installation had been perfect.
Ruckly is still able to understand when the men tease him about his wife, but he cannot do anything violent as before when he was "a holy terror," attacking the orderlies at every turn. On the other hand, Ellis is pretty much a vegetable after his electroshock therapy, proving that such "therapy" is not any effective cure to mental illness. In addition, the cruelty of the institution is exemplified as Ellis is nailed to the wall during the day, urinating on himself because no one tends to him.
Ellis and Ruckly are two Chronic patients who, although only minor characters, serve as demonstrations of the horrific ways in which residents of a mental institution are treated.
Ellis used to be labeled as Acute, but due to the effects of the excessive electroshock therapy sessions he is put through in the "Shock Shop," he becomes a Chronic. He is degraded by being nailed to the wall during the day, which results in him frequently wetting himself.
Ruckly has undergone a parallel experience, with a shift from Acute to Chronic being caused by a botched lobotomy (a surgery that severs parts of the prefrontal lobe of the brain, meant to treat mental illness).
The Chronics also serve as warnings to the Acutes of what can happen if they misbehave and get sent to shock therapy. They are representations of patients who have been damaged past the point of no return.
The author includes so much detail about these two minor characters because he showing the reader the terrible things done to inmates in mental institutions and it also foreshadows McMurphy's fate.