The following didn't directly happen to me, but it came close. I'm using first person anyway for clarity.
A paper is submitted to a journal for which I'm an editor. During review, it's noticed that the paper is plagiarized. The plagiarism is relatively minor and benign: only a few paragraphs are plagiarized, the plagiarized text is in the Introduction and involves only non-crucial background information, and the text was rewritten to the extent that it's not detectable by automated plagiarism checkers. But the text is still plagiarized (see edit below for example).
The paper has several authors, one junior (an undergraduate) and several senior (professors). It's difficult to believe that any of the senior authors would have done this, so a guess is that the junior author wrote the offending text without realizing that this kind of rewriting is still plagiarism, and the senior authors didn't notice.
Clearly the journal should do something, but what? The obvious thing to do is to alert the corresponding author and let them handle it, but 1) there's a nonzero chance that they are the one that is responsible for the plagiarism, and 2) I am concerned about potential damage to the junior author's career, since this will likely alert all the authors to the plagiarism & potentially also trigger institutional academic misconduct policies, and the paper looks like a good piece of work otherwise.
Edit: Here's an example of how the plagiarized text looks. Take this sentence from the above:
The plagiarism is relatively minor and benign: only a few paragraphs are plagiarized, the plagiarized text is in the Introduction and involves only non-crucial background information, and the text was rewritten to the extent that it's not detectable by automated plagiarism checkers.
And the rewrite looks like:
Only a few paragraphs are plagiarized, and in a non-malicious way: the affected text is located in the Introduction, providing background information to the problem, and was paraphrased to the extent that plagiarism detectors are unable to spot it.
The ideas involved are the same, some distinctive phrases are reused, and the text is immediately recognizable if you also have access to the original; but it's substantially rewritten and difficult to detect.