care must be taken when answering this question
 

Usually, I write :

One sometimes cannot find the subject of a sentence when reading a Chinese book.

to lengthen it:

One sometimes cannot find the subject of a sentence when one is reading a Chinese book.

The subject of the sentence is omitted but remains the same.

However, I found a sentence in a university textbook:

Care must be taken when answering this question.

to me, it means:

Care must be taken when care is answering this question.

Do you think this sentence structure is grammatical?
(though understandable)

Re: care must be taken when answering this question
 

It's fine. The active concept expressed by the main clause is retrievable from the passive verb : Care must be taken = you must take care. Therefore the subject of the active non-finite verb "answering" is assumed to be you : ... when you are answering...

Re: care must be taken when answering this question
 

have you ever found such a sentence justified as grammatical?

I have never.

I especially emphasize "grammatical" because if we want to prove our sentence correct so as not to lose marks, we students must invoke authoritative grammars.