If it's an important part of the story, then the author should find a way to add this part. Letting go important parts of a story would change the story considerably and probably make it flat or even incomprehensible, I think.
Sometimes, though, parts suddenly don't fit in anymore. The story I submitted to the anthology was part of a longer story, for instance. When rewriting this story, I found the side story was distracting from the main plot. I rewrote the story and made a whole new story of the omitted part. I have lots of parts and drafts that I hopefully can weave into future stories.