Legally....
Well, in every country I know of, there is no limitation on when you can be charged for murder. Especially not this kind of premeditated "first degree" (as Americans say) murder.Is Korea really different in that regard?
According to Yahoo, the statue of limitations for murder in South Korea was fifteen years before it was extended to twenty-five in 2007, exactly as portrayed in the film. Last year, it was altered again and now there is no statue of limitations for murder.
https://www.yahoo.com/news/south-korea-removes-statute-limitations-murder-041530520.html