I found this article on Wikipedia that claims after a mistress of Il-Jong was found with another lover, he tied her to a pole and publicly executed her. I noticed that the article largely draws from a book called Kim Jong-Il Production: The Incredible True Story of North Korea and the Most Audacious Kidnapping in History. This doesn't seem to be an academic source at all, and also, I can't find mention of any other sources mentioning the incident but this book.
So, does anyone know if this is even true? Has anyone in the history field written about it? I'm just so confused. I'm not even sure if the woman herself exists at this point.
Edit: I accidentally referred to Il-Jong as Il-Sung in the title. My bad.
A minor correction before I start - the former North Korean leader's name is Kim Jong-Il, not Kim Il-Jong.
A Kim Jong-Il Production's author, Paul Fischer, attributes his account of Woo In-Hee's execution to three main sources: interviews with North Korean defectors, North Korean Cinema: a History by Johannes Schoenherr, and Choi Eun-Hee's memoir The Kingdom of Kim Jong-Il. Upon looking at Schoenherr, it turns out that his sources are also North Korean defectors, so that really just leaves us with defector accounts and Choi's memoir.
The Kingdom of Kim Jong-Il has never been translated into English, and my Korean is rusty, but as far as I can tell from the excerpts I tracked down, Choi Eun-Hee (the South Korean actress that Kim kidnapped and forced to make movies) heard the story of Woo's execution from the North Korean filmmakers that she and her husband worked with. While she was in North Korea at the time Woo was killed, Choi didn't actually witness it herself (nor could she have, as she was in prison).
This is the problem when assessing the veracity of the story - every account of Woo's execution is hearsay. Plenty of North Korean defectors have corroborated the event, but none of them actually saw it, and so we are left with the tale of a very public execution in front of 6,000 people and yet no eyewitness accounts. We can assume it to be true, as it's certainly widespread enough in North Korea and there's no record of Woo ever being seen or heard from again. In fact, North Korea attempted to completely eradicate her from their cinematic history, going so far as to edit her out of movies even when her absence rendered them incomprehensible.
While the story of Woo's execution is probably true, there's some speculation around Kim Jong-Il's motivation for ordering Woo's death. While it would be easy to dismiss it as mere jealousy, there's also the possibility (raised by one of Schoenherr's interviewees) that Woo was executed for not keeping her mouth shut. Her affair with Kim was supposed to be completely secret - not just because both of them were already married, but also because Woo had a history of affairs and sex scandals that Kim did not want publicly linked to him.
This came to a head in the summer of 1981, when a half-dead Woo was found in a car with a definitely dead lover after both had suffered carbon monoxide poisoning. Naturally, the police had some questions, and Woo invoked Kim's name to try and get herself out of trouble. This backfired spectacularly. North Koreans say that she was still calling for Kim right up until the firing squad pulled their triggers.
TL;DR - it's probably true, although Woo was likely killed less out of jealousy and more because she publicly outed her affair with Kim.
Sources:
Shin, Sang-Ok and Choi, Eun-Hee. 김정일 왕국: 홍콩 평양 비엔나 탈출까지 (The Kingdom of Kim Jong-Il: Hong Kong, Pyongyang, Vienna, and Our Escape). Seoul: Dong-a Ilbo, 1988.
Schönherr, Johannes. North Korean Cinema: A History. Jefferson, NC: McFarland Publishing, 2012.
Fischer, Paul. A Kim Jong-Il Production: The Extraordinary True Story of a Kidnapped Filmmaker, His Star Actress, and a Young Dictator's Rise to Power. New York: Flatiron Books, 2015.
Armstrong, Charles. "The Origins of North Korean Cinema: Art and Propaganda in the Democratic People's Republic." Acta Koreana 5 (2002). 1-19.