Il-woo and Baek-hee knew each other in childhood, they just didn't recognize each other. Baek-hee's father kidnapped Il-woo, which is proven by several flashbacks already. Especially the latest one (Il-woo's eye color is the same as the little boy's. Plus, clearly the scar on his shoulder that he's always scratching.)
Il-woo came to Gicheon with the excuse that he is going to kill someone, and then himself. This person is probably Baek-hee's father.
(I do hope, the one who wanted to kill is not Baek-hee, because he didn’t help him, he instead hid away.)
In an earlier chapter, on the roof, Il-woo even asked Baek-hee if there is a criminal living in Gicheon. Although I don't know for sure, when they moved in together for a while, why didn't he recognize the apartment, provided it was the same apartment where they were abused in childhood (Il-woo was looking for a house earlier before he asked Baek-hee to showhim around.)
I have a feeling that Baek-hee's father killed Il-woo's father... (Il-woo’s dad died in an accident.)
However, I'm really worried that Baek-hee feels guilty for not helping, and his very own father hurt that person he fell in love with, and that's why he’s not gonna tell Il-woo a thing and he’s gonna keep his secret, or even worse, he leaves, before Il-woo wakes up (ah, please, no!) ... I hope they talk it out, sort it out, and stay, just the two of them, but that seems too good to be true for it to be that simple given how angsty this manhwa is.
Are you telling me that Bekhee’s father went to prison because he kidnapped Yang Il-woo when he was a child? That the boy who appears in the flashbacks at the beginning of the episodes isn’t Bekhee, but rather Yang Il-woo? And that the root of both their traumas stems from the same experience and the same person? Damn—I knew Yang Il-woo had gone to Gicheon to kill someone, but finding out he knew Bekhee completely floored me.
What a brilliantly constructed turn of events—a true masterpiece.
I can only imagine the guilt Bekhee will feel when he learns the whole truth: that his own father is the source of all of Yang Il-woo’s misery—the one who triggered a cascade of misfortunes and ruined his life. He’ll likely blame himself for not being able to save him, even though he couldn’t have done anything at the time; just like Yang Il-woo, he, too, was in need of being saved.