At each stage of the very complex process, the government figured out what to do without too much fuss, even operating as a temporary parliamentary democracy.
It wasn't too long ago that this could have gone very differently: seizure of power, military occupation, coups, violence and corruption.
This is Korea's Nixon moment.
edit There's some very serious discussion regarding criminal charges they may now be brought now that she's freed from Presidential immunity.
edit2 For folks who want more background on what this is all about, "Ask a Korean" has done a magnificent job of writing the charges up.
http://askakorean.blogspot.com/2016/11/the-ultimate-choi-soo...
http://askakorean.blogspot.com/2016/12/the-ultimate-choi-soo...