This is an interesting idea, though again we'd be waiting on Richard and Sander to either custom program something like this or find a PunBB module that does so, because there is nothing directly in the admin settings that would allow for such a status flag currently.
The one thing I do wonder though, is what sort of questions? and when would a thread get closed? It's one thing if someone says as Mirage did in the topic further down this page "the core exiles entry has a dead link" and I remove the link and fix it and then it's done, it's however quite something else if someone asks a question that then leads to a discussion. For example, someone the other day asked about the max pain superliam mod and how to install it. I attempted to answer but either the user might want clarrification, or some other people might chime in with their thoughts about the max pain mod or superliam or side scrollers or any of the usual issues that discussion topics get into, and that of course is not something we'd want to discourage.
Likewise, suppose someone turned up in a year or two with the same question, would the fact that the question had previously been flagged "resolved" actually have any baring on them asking the question anew? considering that by then the original topic would be buried somewhere in the pile.
Or did you just propose this as part of the "Site and forum feedback" area rather like bug reports? Since myself and the other mods manifestly do! check that area anyway and respond to threads, and again we prefer not to close topics unless there's a really good reason to do so.
So while I'm certainly not against the idea I think we'd need to consider firstly if it's possible, and secondly when, where and how on the forum it might be helpful.
With our dreaming and singing, Ceaseless and sorrowless we! The glory about us clinging Of the glorious futures we see,
Our souls with high music ringing; O men! It must ever be
That we dwell in our dreaming and singing, A little apart from ye. (Arthur O'Shaughnessy 1873.)