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He died of lung cancer. And tbf it feels like just a random reason author came up with for it. Later on there is an incident with fire where Soohan comes out pretty much unscathed and the doc comments how his genetics makes him resilient to smoke inhalation. Then Soohan sort of fondly? remembers that his father once saved Yeonseo from fire and although he had quite a few burn injuries that lasted quite long and reopened multipke times, he was fine after all that smoke inhalation. Also its wierd that Yeonseo's parents didn't pay or managed to get him skin grafts considering they are pretty decent people.
Omg how did the father die? And I wonder if it had a negative impact on soohan