expression
out of luck; end of one's rope
Used when someone's luck has run out, often in a dramatic or resigned tone. Common in phrases like 運の尽きだ.
ここでエンジンが止まるとは、運の尽きだ。
The engine dying here means we're out of luck.
彼は最後の試験に落ちて、運の尽きだった。
He failed the last exam and that was the end of his rope.
運命 is a neutral noun for 'fate' or 'destiny', while 運の尽き is an idiomatic expression specifically for the moment luck runs out.
不運 means 'misfortune' or 'bad luck' as a general state, whereas 運の尽き emphasizes the finality of one's luck ending.
From 運 (luck) + の (possessive particle) + 尽き (noun form of 尽きる, 'to run out'). Literally 'the end of luck'.