Why you shouldn't change a question with answers
Changing a question in substantive ways after answers have already been posted, anywhere on Stack Exchange, is likely to make those answers obsolete. In general, this should be avoided when possible; changes may make part or all of the answers irrelevant, or worse, invalid. This can even negatively affect reputation for the people who answered the original question in good faith, only to have the question changed in a way that turns the answer they spent time and effort to provide into a response that is now not helpful or is perhaps even completely wrong.
One of the very real purposes for comments is to suggest ways to improve a question—to ask for information that would be needed to provide a better answer, or to suggest ways to make the question more clear or more useful to other visitors. And edits can be made, or at least suggested, by anyone. That questions may change is part of the model here; there's even a bounty reason to attract interest back to a question whose existing answers may have been made obsolete by changes (to the question, or to reality):
Current answers are outdated
The current answer(s) are out-of-date and require revision given recent changes.
In other words, nobody is saying one should never ever change a question just because doing so might affect answers that have already been posted.
So when is it okay?
A lot of us are here because we are fans of puzzles, puzzle-solving, and puzzle-creation, and this is a great community in which we can try to improve our puzzling skills. Insisting that every puzzle be perfect when posted is unrealistic, and as mentioned, isn't really even within the spirit let alone the letter of the "rules" on how Stack Exchange works.
- If your puzzle is broken, and you think it's worth salvaging it, then salvage it.
- If you think the level of wasted effort already put in by those attempting to solve the puzzle in its broken state is too high a price, then let it go.
Ultimately, it's a balancing act between being fair to both the puzzle and its solvers by making the puzzle actually solvable as intended, and being fair to both the existing answers and their writers by not turning them into so much wasted effort. When it's a relatively small part of the puzzle that needs to change, such that most of the work spent by solvers in pursuing and writing up their solutions is still relevant and valid, this points pretty strongly to making the change. It's a good idea to briefly point out the change and that it was done to fix the puzzle (not to move the goal-posts). As long as this isn't a pattern with you, the community is generally understanding—like I said, we're here to learn, and sometimes learning is as much about making mistakes as doing things Just Right.
But if the puzzle as originally posed cannot be meaningfully salvaged without essentially starting over—changing it into something completely different—letting it be closed as too broad is probably the fairest fate for it, for all involved. At that point the best option may well be to close it, and then post a new question with the refined version. This won't invalidate any answers on the too-broad puzzle, and allows for a fresh start with a more polished question that can accumulate appropriate answers. You'll want to ensure the new version is sufficiently different from the original to not end up being closed as a duplicate of it—but you wouldn't be pursuing this route if you weren't making huge changes anyway, so this shouldn't be a problem.
Do be aware that making significant changes to a puzzle to salvage it is likely to not sit well with people whose efforts to solve it are now in vain—so don't be surprised if their unhappiness manifests itself in downvotes. Leaving a too-broad puzzle unchanged, on the other hand, will probably garner not only about the same downvotes but also be closed, which makes it highly unlikely to gain any further positive votes. This might feel a little harsh to someone who's still trying to improve, but at the end of the day, upvotes and their accompanying Imaginary Internet Points are the reward for questions and answers that are actually successful, not just for ones that tried really hard. If gaining reputation here is part of what motivates you to post puzzles, then this should motivate you to really polish your puzzles until they shine, before you post them.... and that benefits everyone here.
Note to solvers
Let's face it, most of these too broad puzzles look like they're going to be too broad right from the start. Sometimes people even post putative solutions that actually fit the puzzle as posted, but which the answerer is pretty confident is nothing resembling the intended answer, just to make the point about the puzzle being too broad. If you choose to answer a puzzle that looks too broad, then don't be surprised or upset if the question is edited and your answer is now excluded as intended, and perhaps ends up drawing downvotes or needing to be deleted. Much better would be to try to help the poster recognize the issues with their puzzles via constructive comments, and to vote to close until those issues are satisfactorily resolved.
Closing a puzzle is not a punishment - it's the best mechanism we as a community have available to us to prevent people spending time and effort on a flawed puzzle that is likely to either be substantially edited, or (perhaps eventually) deleted. It's meant to help the poser refine their question so that it can be solved the way they intended. Use it, please!