The Junkman could have done it.

It’s possible he lied to the Mother. He was present at the re-enactment crowd where he says he saw the Son and confirmed he was definitely the killer. At that same re-enactment, the Mother was giving out fliers and exclaiming her son’s innocence. It’s totally possible he saw the Mother saying this and remembered her face, which is why he claimed to have seen her before. I know he could have remembered her from the umbrella encounter, but seeing her at the re-enactment and knowing that she’s Doon-Jo’s mother would be more memorable. Recognizing her, he probably thought it would be best to gaslight her into believing her Son did it, which is why he didn’t completely overreact to her overreaction to his fable. He already lied about his reason for being there, and sleeping with underage girls is also a sign of an unstable mind. He also lives completely alone in a junkyard. Furthermore, he is seen mixing something into the rice he was going to give to Ah-Sung, suggesting he was up to something. Perhaps he knew about his picture in her phone, and killed her to avoid public shame. We already know he feels shameful about it since he lied to the mother about why he was at the murder scene. It’s also completely possible that word of Doon-Jo’s overreaction to being called a “retard” became more widespread than just the prison, as well as his recollection technique of rubbing his temples. There’s reasons I feel that the ambiguity of the true identity of the murder makes this movie amazing, and both possibilities of the son being the murderer and the junkyard being the murderer, are both deep endings in their own ways.