The Daily NK, an online publication in Seoul with sources in North Korea, reported that three teenagers had been sent to a re-education camp for cutting their hair like K-pop idols and hemming their trousers above their ankles. The BBC cannot verify this account.
All this is because Mr Kim is in a war that does not involve nuclear weapons or missiles.
Analysts say he is trying to stop outside information reaching the people of North Korea as life in the country becomes increasingly difficult.
Millions of people are thought to be going hungry. Mr Kim wants to ensure they are still being fed the state's carefully crafted propaganda, rather than gaining glimpses of life according to glitzy K-dramas set south of the border in Seoul, one of Asia's richest cities.
The country has been more cut off from the outside world than ever before after sealing its border last year in response to the pandemic. Vital supplies and trade from neighbouring China almost ground to a halt. Although some supplies are beginning to get through, imports are still limited.
This self imposed isolation has exacerbated an already failing economy where money is funnelled into the regime's nuclear ambitions. Earlier this year Mr Kim himself admitted that his people were facing "the worst-ever situation which we have to overcome".
The Daily NK was the first to get hold of a copy of the law.
"It states that if a worker is caught, the head of the factory can be punished, and if a child is problematic, parents can also be punished. The system of mutual monitoring encouraged by the North Korean regime is aggressively reflected in this law," Editor-in-Chief Lee Sang Yong told the BBC.
He says this is intended to "shatter" any dreams or fascination the younger generation may have about the South.
"In other words, the regime concluded that a sense of resistance could form if cultures from other countries were introduced," he said.
Choi Jong-hoon, one of the few defectors to make it out of the country in the last year, told the BBC that "the harder the times, the harsher the regulations, laws, punishments become".
"Psychologically, when your belly is full and you watch a South Korean film, it might be for leisure. But when there's no food and it's a struggle to live, people get disgruntled."