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I have a hard time understanding the meaning of the following question:

Who could have taken my coffee? I thought I was the only person in the office today!

All grammar books say that the structure "Could have + past participle" means that some situation was possible in the past, but it didn't happen.

Basing on this rule, I make a conclusion that the coffee is still there and was not taken by anyone, but the rest of the phrase makes it clear that the coffee was actually taken.

What is the correct meaning of the sentence? Is the coffee still there?

The same thing goes for the following question:

How could I have forgotten to pay the rent?

What does this question imply? Did I forget to pay the rent or I paid it?

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  • That's a very common use, but could is a modal auxiliary, and they all have multiple uses. Don't believe any grammar book that attempts to tell you what anything "always means" -- there are always exceptions and other things that the authors either were ignorant of, or thought their readers were better off not knowing about. Commented May 7, 2022 at 23:08

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Your book doesn't tell the whole story.

Could have generally has its counterfactual meaning if it follows a counterfactual conditional (though that conditional is not always explicit).

eg

You could have broken your neck (with an implied If you had fallen off what you were climbing on).

In a WH-question, this condition does not usually hold, so that interpretation of could have does not apply.

There are still two possible interpretation of the construction.

A detective might ask He got in and out without setting off the alarm. How could he have done that?

Here, could has its usual (deontic) meaning of being able to do something (effectively, the past of can), and the detective means "How was he able to do that". (The detective might also have asked How could he do that? - simple past rather than past perfect: as usual the difference is in whether the detective is setting a temporal focus point and looking back from it to the events or not).

But more commonly with could have, could has an epistemic meaning, about the speaker's knowledge or expectations. Who could have taken my coffee doesn't normally mean "Who had the ability to take my coffee?", but something more like "Who is there that might take my coffee" - it's a rhetorical expression conveying surprise or disbelief.

This is even more so in your second example: How is it possible that I failed to pay my rent? with that surprise or disbelief.

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