On the question I am looking for the author of a trilogy the OP user13147 seems to be deleted.
So there is no hope to identify this "Sci-Fi trilogy" as the user cannot respond.
How should we handle such questions? Should they be deleted?
The main benefit of a good story identification question is to provide information to other users who may also be looking for that story.
Therefore, it doesn't matter if the OP deletes or not (in fact, its not really any different from a Story ID question where the OP leaves soon after asking, and doesn't come back. Or even asks and doesn't bother checking to see if they got an answer.
I don't think anything special should be done if the OP deletes.
Those question are hopeless and wont get an answer, if someone is searching for same story, It would be better if he ask a brand new question, otherwise, he will just find this question and pass on. They are dangerous dead-end on the information highway and a roadblock must be put on the path before someone hurt.
Anyone who think he may have fond the solution is destined to eternal doubts, no one will be able to confirm the exactitude of this finding. Those are desert island where someone surfing on the internet could only be washed up without any hope of being saved.
They are dangerous for the health of the website, they are like a rotten corpse and need to be buried before the plague destroy the village. They need to be DESTROYED!
TO THE STAKE!
I'll propose a solution mid-way between the two extremes presented by esteemed previous answerers. They both make some good points:
Such questions IMHO aren't as A-OK and inoffensive as @Beofett thinks, under the general ideas presented by @DavRob.
We routinely close questions that can not generate "correct" answer (when any possible answer is just a guess) as NC or NARQ; and an orphaned "story-id" question by definition can not be "correctly" answered, since the correctness is only known to the
beerholder OP who's gone, gone, gone.
On the other hand, @Beofett presents a compelling argument in the comments to @DavRob's answer, that deleting such questions is problematic because some of them contain good (even if not provably correct) answers, which contain useful information for future readers AND cost people answering them a lot of time and effort researching (and as a secondary consideration, gave them rep).
Therefore, I would propose a more nuanced policy:
If such an orphaned story-id question has no answers (or all of answers are obvious shoot-from-the-hip meritless guesses with no useful info in them whatsoever - e.g. not showing how such a guess matches the question).
If such an orphaned story-id question has an answer that appear to contain useful information and show effort (and when choosing between #1 and #2, I would recommend heavily erring on side of #2 if answers are present)
... then close, but do not delete such a question.
I'm agnostic as to what close reason we use (Not Constructive or NARQ can be applicable; I would argue against T.L.).
P.S. If the only concern over adopting this policy is the subjectiveness of "has good answers" vs "has bad answers" criteria, we can easily institute objective criteria for that.
An answer to an orphaned story-id is considered "good" if:
It has 3 or more up-votes.
OR, if (no matter how voted), it presents an explanation how the work in question matches point-by-point description of the work in the question - thus giving the readers a clear way to see if, at the very least, the answer is "possibly correct".
Please note that "matching point by point" does NOT have to be 100% positive matches - personally, an answers that honestly says "this work matches point #1, #2 and #4 because of xyz plot points; but does NOT match OP's point #3" is a good answer even if it's probably not a "correct" one.
An answer to an orphaned story-id is considered "bad" if:
It merely presents the name of the work, without showing how that work matches OP's question.
Or, it is clearly wrong (e.g. comments show many points in which it does NOT match OP's question, which the answerer didn't even consider).
An answer that isn't clearly "bad" under the above rules, should be assumed to be "good" - in other words, the question should NOT be deleted (but still closed).
Again, to re-iterate, this policy should strongly lean in favor of assuming the answers are "good", i.e. closing as opposed to deleting OP's question.