A search in Youtube for 끝내기 does not show any Go (game) lecture videos. Therefore perhaps this Korean translation for "endgame" isn't the best translation.
Well, that is the term in Contemporary Go Terms by Nam Chihyung, who would know. It is not a translation, BTW. :)
There have been some criticisms of Nam's English equivalents of CJK terms. Yahoo's Babelfish translates these Korean symbols as "ending" which, to my mind might not be the same as the phase of the game we call the endgame. Ending might just be what we call the result, for example. When I Googles this Korean word I got several sports-related references, soccer for example, and I don't think any part of a soccer game matches up with what we'd call the endgame of a game of go.
The Korean rules use different terms for the end of the game:
"Section 4. Jongguk (the end of the game)
"Article 15. Daeguk Jongryo (the end of the endgame)
Daeguk Jongryo is reached when there are no profitable moves left.
"Article 16. Jongguk
After Daeguk Jongryo, neutral points are filled and Jongguk is attained. The neutral points are filled alternately unless other agreement is made."
From http://go.yenching.edu.hk/
Translating back and forth among Japanese, Korean, and English Nam equates yose and kkeunnaegi (the word on this page) and endgame; she equates shuban and jongban and closing stage.