〜ずじまい
ended up never (doing), never got round to
Verb ない-form minus ない + ずじまい(だ · で)
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ずじまい means you intended or hoped to do something, but the chance passed and it never happened: 忙しくて、結局その映画は見ずじまいだった, "I was so busy that I never did get to see that film".
Build it like ずに (N4): 見ない → 見ずじまい, 聞かない → 聞かずじまい. する becomes せずじまい. It works with potential verbs too: 会えずじまい, "never managed to meet".
It's usually in the past (ずじまいだった) and carries regret. 結局 ("in the end") often comes before it.
Compare ずに ("without doing"), which is neutral, and 損ねる (N2, "missed the chance"), which is about one occasion. ずじまい is about it never happening at all.
Examples
忙しくて、結局その映画は見ずじまいだった。
I was so busy that I never did get to see that film.
彼女の名前は聞かずじまいだった。
I never did find out her name.
せっかく買ったのに、一度も使わずじまいだった。
I bought it specially, and never once used it.
本当のことは言わずじまいだった。
I never did tell them the truth.
結局、彼には会えずじまいだった。
In the end, I never got to see him.