The Jeju incident seems like suicide is the key

To be honest, based on the news and gossip from a few days ago, I thought it was a homicide.
But if the neck was tied with a rope and that rope turned out to be Mr. Jang's shoelace,
for it to be a homicide, the perpetrator would have had to kill Mr. Jang,
go to Mr. Jang's house to get the shoelace, and then return to the crime scene
to move it or something like that.
Setting aside how incompetent the police are, suicide seems more likely based on the circumstances.