I've always gone back and forth on this question. I understand that at least to some degree, the answer is going to be based on context. However, I'd like to know what others think as well. Here's a sentence I'll use as an example: Jan sat at a table in the library surrounded by stacks of old files and books covered with dust that made her nose itch. The clause, "that made her nose itch," refers to what, exactly? I wrote it to refer to the dust. However, when I read it again, I realized that without any other commas, it is at least possible to read this line as both the old files, and dust-covered books making her nose itch. So, when you all read something like this, how do you determine what is being referred to?
Ah well...looks like what you got going there is, "Snatching defeat from the arms of Victory." It doesn't matter because the reader will be onto the next sentence before a question like that would pop-up in their head. 'Course, that means that the question won't pop-up in their heads because they'd be thinking of the next sentence, and the next...get it? Don't throw the baby out with the bath water. All's you have to do is keep them reading.
As I interpret this: Dust is making her nose itch. The same dust is covering stacks. The stacks are composed of files and books. The files and books are old. The main ambiguity for me is whether the books, as well as the files, are old. I realize that other ambiguities include: Whether the books are stacked. Whether the files are dusty. but I find myself making the above assumptions anyway; I had to go out of my way to find those other ambiguities.
Ya know...there is a interesting thing the brain does--it fills in extraneous data automatically...so the writer doesn't have to. That also means that you do not have to explain stuff everyone knows. Like explaining just exactly--in every imaginable way--what kind of a bright and sunny day it is. You can simply write, "It was a bright and sunny day."
. In your above example it probably wouldn't matter as the whole image is one of dust and must. But it's still a sentence that would benefit from dividing and therefore clarifying precisely what made her nose itch. E.g. Jan sat at the library table surrounded by stacks of dusty old files and books. Dust that made her nose itch. Or, Jan's nose itched from the musty old files and books that surrounded the library table. Plenty of ways it can be written so that the meaning is specific and the sentence not too long.
For me, the meaning is actually not to bad as it is. We have Jan, sat at a table in a library. On that table (and by implication other tables too, and maybe even on the floor and window sills as well) are stacks of old files (old implies they might be covered in dust) and stacks of books (also old by implication) and as described covered in dust that makes Jan's nose itch (by implication that is the dust doing that as the old files and books are highly unlikely to be making Jan's nose itch). What remains is flow: Jan sat at a table in the library[,] surrounded by stacks of old files and books [that were] covered with dust that made her nose itch. Of course, there are several ways to break up the sentence, my edit above is just one.
A clause only needs clarifying if there can be a degree of confusion. This doesn't apply to the example used, which is perfectly clear in its original form. As has been said, the reader fills in the gaps. Further, the reader rules out the impossible: you could argue that in the original the library was surrounded by books.
The clause binds to the nearest preceding object by default. In you example, that would be dust, which is what you intended. Often, you'll see sentences in which the clause is not adjacent to the object it is meant to bind to, with hilarious meaning if you interpret it as belonging to the nearest object.
Don't think there's anything actually wrong with your sentence - yes I'd assume it's the dust that made her nose itch. Personally, though, I'd say that sentence is a little clumsy at least. It's not a bad sentence, but it could be better - as it stands it feels a little run-on. I'd separate it into 2 sentences: Jan sat at a table in the library surrounded by stacks of old files and books. They were covered with dust, which made her nose itch.
I wouldn't separate it into 2 sentences, I'd just edit and revise slightly. Jan sat in the library surrounded by stacks of old files and dust covered books that made her nose itch.
See, that's what I thought, and how i usually read/write things. What made me start wondering however, is the "and" in the sentence linking the books and files. Funny though, now that I've read your post and went back to the original sentence, it does seem much clearer again. Maybe it was just a moment of spending too much time looking at something and not seeing the forest, just all the individual trees.