They have left NewYork for good;They'll never go back and live there again.

他们永远离开了纽约。他们再也不会回到那里住了。
for good 是永远的意思。

foor good：永远
“I can't believe that you cheated on me again!! Enough!! I'm not gonna take this any more!! We are done for good!!”
“我不敢相信你竟然又偷人！！够了！！我再也不能忍受这种破事了！！我们之间完了，永远完了！！”

for good 永远的意思

for good [简明英汉词典]
永久地,一劳永逸地

FOR GOOD may be a slang.

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