You may have noticed that I tend to re-tag a lot lately. However, I only re-tag questions that aren't closed.
But now I'm wondering, should I also re-tag closed questions? Is this useful? If it's not, why do we keep those question around at all?
If the question is closed as duplicate or too broad, then tag it properly.
Tags are defined as :
Using the right tags makes it easier for others to find and answer your question.
Closed may not be answered, but we can try to salvage it by removing objectionable content. Sometimes, a moderator or other experienced with site's scope may perform a heroic edit. So, edit the tags. This would not push the question into reopen queues. Even if that happens, you can just select "Leave closed". It's not much a problem. Not only tags, if you can improve title or body than existing one, go ahead.
If the question is closed (and not put on-hold) as Off-topic or "Unclear what you are asking" and question is not possible to salvage the post in anyway, then the proper way is to cast a delete vote rather than retagging. That only extends the life of that question.
See When should I vote to delete a question from Meta Stack Exchange.
If you see a closed question that needs to be re-tagged, you should do so. If it's a question that can be salvaged via edit, re-tagging will bump it to the front page and increase the chances that someone will see it and take the time to fix it (you could of course make the necessary edits to make it on topic while you are re-tagging if you so desire). If it can't be salvaged, you should also vtd in addition to re-tagging. Re-tagging will still bump the post to the front page, where other users might see it and vtd as well.
Questions that are kept around via the historical lock are not able to be edited, so you won't be able to re-tag them.