Not possible. They are part of the chaebol [1], meaning they are essentially part of the South Korean government. They can't really fail as long as the country exists. There's an old joke that South Korea isn't really a country, but five families/companies pretending to be one and there's some truth to this.
It is possible because South Korea does not have control in other states.
Even if chaebol is powerful they still heavily depend on export profits. They can't help themselves if EU/USA consumers and governments take this scandal seriously.
Remember the story about the South Korean female president or whatever their title is being a brainwashed puppet of a radical feminist cult and thus had to abdicate as this came out? I don't remember how many years ago that was, but it's not like their education prevented the situation.
[1]: https://en.wikipedia.org/wiki/Chaebol