I have to say that there has been a marked decrease in posts that have not been answered reasonably promptly, and this is due to an increase in Community Champions and a new method by Moderators. That is not to say it might never happen, particularly if a new poster posts on the end of an existing thread, but overall the situation is better.
Should you find a post that has gone unanswered for an excessive time (and here I do not mean just a day or so) then by all means report it, or if you feel it is appropriate pop a response in yourself - it does not have to be long, though your posts are pretty spot-on and helpful.
(As there is a constant search of unanswered posts which are a day or so old they are normally picked up anyway)
In relation to the change of Section for a thread, yes they can be placed in a more appropriate place, often promptly. This as you would appreciate is to get potentially distressing matters out of the Welcome Area and at the same time, by placing the thread in a more appropriate Section increase the chances of the poster attracting attention and being replied to.
I'm not sure how to overcome this difficulty if you have not posted, perhaps simply making a note of the poster's name or thread name and searching for it. If you have in fact posted in a thread and it is moved your link should remain valid in your My Threads list.
I don't know if that helps at all, I hope so