The real solution to this is to make a button to mark as unresolved, or something to that effect. I don't even like contacting a moderator as a solution, the middle man shouldn't be necessary at all.
To address your question though, they should do these things if they want more attention on their question:
- Leave a comment on the answer expressing its inadequacy. The person who made it might update it, or someone else could answer instead.
- Add a clear notice to their question title indicating it isn't resolved. This could be as simple as throwing [UNRESOLVED] onto the end.
- They could add the
unresolved tag to their question, which is lesser known now but used to be one of our solutions for posts that fit the category you described.
All of these things will hopefully attract attention from other users with extra privileges, who might flag the post for staff attention, convert it to a comment or take it down outright. But there should be a way for askers to get their posts on the unanswered list by themselves.