鍵を持たないで、家を出てしまいました。

[healer]

While ~てしまう has the completion and irreversibility referred to the action indicated by the verb, the sense of regret refers to the feeling of the speaker, doesn’t it? So the subject of the sentence might not be the speaker.

The above sentence from a textbook is saying the speaker or anyone else left home without the key. The sense of regret is on leaving home. If I want to put the regret on taking no keys, is the following sentence I made up possible and grammatically correct?

家を出て、鍵を持たないでしまいました。

By the way would you say いえ or うち for the kanji 家 above?

 

[Toritoribe]

The subject regretted having left home without the key, not just having left home. You should think it's like 「鍵を持たないで、家を出て」しまいました.

The -te form is used to list events in the temporal order, including "at the same time". Thus, 家を出て、鍵を持っていないことに気付いた is OK, but 家を出て、鍵を持たなかった sounds odd.

As for the negative form of ～てしまう, ～ないでしまう is rarely used. Instead, other affirmative expressions in similar meanings like 鍵を家に置き忘れてしまった or 鍵を持つのを忘れてしまった are used.

Incidentally, ～てしまわない is only used for incompletion, and not for unregretfulness.
e.g.
昨日のうちに宿題をやってしまわなかったので、今日もやらなきゃいけない。

By the way would you say いえ or うち for the kanji 家 above?

Both are possible.