What exactly is your situation. What you say is not true. There are ways you can safely edit a question after the quiz has been attempted. There are also ways you can break things by doing that. Hence, we need to know exactly what sort of change you want to make.
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First, I acknowledge that the problem described in your first paragraph is a serious usability issue. (That is an understatement!) Unfortunately, I don't currently have any great ideas for how it could be solved. Of course, the current behaviour is also entirely logical, if you happed to understand the data-model of the Moodel question bank and quiz. (Small comfort for most users.)
Which brings us to the enigma in the rest of your message: why didn't this happen in the other quiz?
I think the only way to find out is to look at the data - if you want to spend some time rooting around in your Moodle database.
The key bits of structure are
mdl_quiz <-> mdl_quiz_slots <-> mdl_question
mdl_question <-> mdl_question_categories <-> mdl_context <-> mdl_course or mdl_course_modules
Sorry, that is a very sketchy outline of where you might need to look. Unfortunately https://docs.moodle.org/dev/Quiz_database_structure is out-of-date.
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Re: Smoothest way to edit quiz after attempts have been made
My guess would be that teacher probably did something different either in the duplication method or in the question changing. It could depend on where the questions were stored originally. If stored in a category specific to the quiz, then I would think the questions should be duplicated to another category. If stored in a course level category, then the questions might not be copied.
Tim, can you enlighten on how the duplication process works? Does it not normally make duplicates of the questions?
If the questions were duplicated in both cases, then I would suspect that the teacher inadvertently edited the wrong quiz..
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Re: Smoothest way to edit quiz after attempts have been made
Duplicate activity works using Backup and Restore. It automatically backs up the activity as a single-activity backup, and then restores that.
As you may or may not know, there is a long-standing issue with backup and restore involving shared quetsions, and from the point of view of a single quiz, questions in the course question bank are shared. Well, it is not really in issue in this case. But, when the questions are shared, the duplicate points to the same questions, rather than making new copies.
As April says, one explanation is the for the quiz that duplicated OK, the questions were actually in the quiz-specific part of the question bank. (And you could check that hypthesis though the Moodle UI. You don't have to dive into the database.)