The following pattern is common on math.SE:
Question Q is posted: is statement $S_1$ correct?
Answer A shows that the statement is wrong, by displaying a counterexample. As far as Q&A of specific questions is concerned, this is a correct and conclusive answer to the question as stated.
Question Q is modified in light of counterexample A: is statement $S_2$ correct?
Correct answer A is now subject to downvotes because it is inapplicable, wrong, or irrelevant to the revision $S_2$, and later readers of the exchange do not see that it refuted an earlier version of the question, except in the rare case when they review the edit history of the question.
More generally, editing questions can improve them but substantial changes to the content can turn the Q & A into a blog which is confusing unless answerers "post defensively" with lots of redundant material in case the Q changes.
The FAQs I have seen do not address the following points:
-- focused Q&A is not a "blog about the topic of the question"
-- advice to questioners on how to operate when editing the question (e.g., explain the change and its connection to any existing answers)
-- advice to answerers on how to avoid confusion when posting (e.g., include material that makes the answer more self-contained). This is not necessarily desirable because placing more demands on the respondents would make it marginally more time-consuming to post answers in some circumstances --- if a stand-alone paragraph is needed where a more context-dependent one-liner might have sufficed, some answers might never get posted.
-- should a refuted (or fully answered in its original form) question be edited, or frozen and with modifications of the question posted as separate threads?