Hmmm I don't think that's it. I haven't read any chapter past 41, but from what I've seen that doesn't really work.
Bum and Sangwoo are only a few years apart so leaving your kid with someone else and moving to a different part of the city seems kinda hard. And if Bum was left with another guardian since he was a baby you would think his uncle would've said things different in his interactions with Bum. And it was already heavily implied that Bum was together with his parents for a while, cause his uncle calls him weak because of the way his parents raised him. His uncle never said snything about Bum's parents leaving him (knowing his uncle he would've totally used that).
If that is the case I feel like that would be a cheap shot on the author, cause that would feel super out of place. The only similarities Sangwoo's mother and Bum have in common is dark hair, skinny figures, and personalities, all traits that can easily be dismissed as logical chance.
Korea is know for most of their natural hair color to be black and brown. Bum and the mother both have a high metabolism and had to deal with starvation so they lost a lot of body muscle. And with their personality has to deal with the situation they were in (both abused).
But hey! That's just a theory, a webtoon theory! Thanks for reading! (●'◡'●)ノ
Whhhhaaattttttt???!!! You mean that dumb little line of "I haven't seen my family in 20 years. You might've well said you were my brother." <- that one line (couple of lines, but still!) If the author what that more clear she should've done a better job! What a cliche! Ugh like every drama has made the to "love" interest into family of so kind! No, I won't expect that (until it is written down in the story itself!)
In chapter 25 Bum's uncle said "Just die like your mother and father" to Bum.
If Bum was Sangwoo's brother it would mean that his parents faked their death, left Bum behind for some reason, the mum became pregnant again immediately and they started a new life with a different identity in the same town without anybody noticing it.
But most importantly: What's the point? There isn't really anything you can make out of this.
If they're brothers then they don't know about it and who is supposed to tell them? Unless somebody already thinks that they might be siblings and tests it even the police wouldn't know since they're not twins (twins have the same genetic fingerprint. That's something you notice.).
But let's just say they somehow find out they're brothers. Would this benefit the story? I've thought about it since the first time someone posted this theory and every scenario I could think of would not add anything to the story besides one "shocking" reveal (unless Koogi decides to change the characters' personalities without any explanation again) or it would even make the story worse because you have to add storylines (like why the parents faked their death) that would only make the story overly complicated and less realistic.
Maybe Sangwoo's mother is actually bum's mother. Remember when bum's uncle was talking about his brother (bum's and maybe sangwoo's father) and his mother in ch.25? That would make sense. They left bum and started new family and that's how sangwoo was born