Yeah, this would be a response to someone saying "꺼져!". So the conversation would go something like this... A: 꺼져! (Get outta here!) B: 꺼져 줄게! ('~줄게' goes on the end of a conjugated verb and means "I'll do 'it' - whatever 'it' may be - for you. So this response would roughly translate to, "No problem, I'll leave). 잘 살아 literally means 'live well', so in this case might translate to 'take care', so the whole thing might be something along the lines of 'No problem, I'll leave. Take care!' but yes, these people are most likely not very happy with each other and 'B' is acting like or she doesn't really need 'A' in his or her life. Some more examples of '~줄게'... 하다 = to do 해 줄게(요) = I'll do it for you. 기다리다 = to wait 기다려 줄게(요) = I'll wait for you. 사다 = to buy 사 줄게(요) = I'll buy it for you. Hope that helps!

Maybe...I leave you and I wish you to be happy. But it is polite expression and only direct translation of 꺼져 줄게 잘 살아. This Korean sentence really meaning(meaning inside) is little sarcastic to leave me.

well actually the person who use this sentence might doesn't have good emotion.... so if i translate that to english 'i sod off, do whatever u want' well 'do whatever u want' is i put instead of real meaning of '잘살아' but in this case that is more similar to emotion of speaker. i hope there's nobody who gonna use that to u :D

Hah! I love sarcasm. In that sentence, 꺼지다 means go away, bug/*uck off. I'll go away for you, live happily. What s/he is really saying is "I'll go away for you, I'll watch if you can live happily."