I'm a Cyborg, But That's OK

The film takes place mostly in a mental institution filled with an eclectic menagerie of patients. Young-goon, a young woman working in a factory constructing radios and who believes herself to be a cyborg, is institutionalized after cutting her wrist and connecting it with a power cord to a wall outlet in an attempt to "recharge" herself, an act that is interpreted as a suicide attempt. Her delusion is characterized by refusing to eat (she instead licks batteries and attempts to administer electric shocks to herself), conversing almost solely with machines and electrical appliances and obsessively listening to her tube radio at night for instruction on how to become a better cyborg. Her apathetic mother is interviewed by the institute's head doctor, to determine the roots of Young-goon's psychosis; despite claiming ignorance of her daughter's delusion (it is later learnt she knew but was too busy to make her seek help), she reveals that Young-goon's mentally ill grandmother had previously been institutionalized for delusions of being a mouse, a trauma that sparks Young-goon's own lapses from reality. As a result, she frequently fantasizes of finding her grandmother and seeking revenge on the "men in white" who took her away.
Il-soon, a young male patient hospitalized for anti-social behavior and kleptomania (stemming from schizophrenia) becomes fascinated with Young-goon; he is described as having "no sympathy" for his fellow man, believes he can "steal" other people's souls/attributes, and frequently wears handmade rabbit masks. He fears that he will eventually "shrink into a dot" and is seen compulsively brushing his teeth when nervous or upset. His habit of covertly taking the traits of his fellow inmates makes him the frequent target of scorn, but he only takes the traits willingly and returns them to their owners after he is done.
When Young-goon persuades Il-soon to take away her "sympathy" in order for her to be able to kill the men in white, she has a hallucination of going on a rampage, slaughtering the doctors and orderlies of the hospital. When she is given shock treatment owing to her refusal to eat, she believes that she has been recharged. In reality, her physical condition begins to deteriorate rapidly, and the doctors begin force-feeding her to keep her alive. Il-soon, now wracked with sympathy for Young-goon, hatches an elaborate plan to get Young-goon to eat, convincing her that he can install a food-to-electrical-energy conversion unit (a "rice-megatron", as he calls it) in her back. After eating her first meal at the hospital, and confiding her secrets to the head doctor, Young-goon ponders the meaning of a recurring dream in which her grandmother explains to her the purpose of her existence. Interpreting the lip-read message as that she is in fact a "nuke bomb" that requires a bolt of lightning to detonate, she goes out into a horrendous storm with Il-soon, intending to use her radio's antenna as a lightning rod.
In the middle of the storm, the wind blows their tent away, prompting them to hastily protect their food supplies. Il-soon, hearing Young-goon's complaints about the opened wine collecting rain, plugs it with his little finger. Unknown to Young-goon, it is shown Il-soon placed the missing cork atop the makeshift lightning rod, protecting her from lightning; similarly to using the 'rice megatron' to make her eat, Il-soon did so to protect her without discouraging. Sitting together as the sun rises, the duo soon embrace under a rainbow.

Question: Who does Il-soon feel sympathy for?
Answer: Young-goon