grammar - Can we use negative form before ～てしまう : f.ex. なく+～てし まう？

Using the form ～てしまう we mean, that something happened in a way we did not expect. But what if we use a negative form before the ～てしまう ending? Will it be also grammatically right?

For example:

昨日メッセージを書いていなくてしまいました。

Answer

なくて doesn't connect to しまう but ないで does, in other words, you can say 昨日、メッセージを書かないでしまった.

(Technically, 書いていないでしまった is possible but that sounds very awkward. On the other hand, 書かないでいてしまった is fine though I still can't see the point to use it here.)