Dear NT:

You wrote:
> My problem is with negative sentences followed by a clause of purpose:
>
> 1-I didn’t go out tonight (,) to study for my exam.
> 2-I didn’t turn off the light (,) for you to be able to read.
> 3-I didn’t make a noise (,) so that he wouldn’t notice me.
>
> A-Are the commas necesary?
> Can’t there be cases where the absence of a comma might cause ambiguity? (I didn’t go out to study. I went out to have fun.)
> B-Can one use a comma in all of the above sentences?

First of all, the first two sentences really are not good English at all–they are awkward, ambiguous, and hard to understand.

This is what I think you want to say:
1. I didn’t go out tonight in order to study for my exam (weak but understandable).
I didn’t go out tonight so I could study for my exam. (typical and understandable but informal)
I didn’t go out tonight so that I could study for my exam. (standard English) No comma is necessary because the subordinate adverb clause follows the main clause.

2 I didn’t turn off the light in order that you could (or “would be able to”) read. (OK)
I didn’t turn off the light in order for you to read. (informal)
I didn’t turn off the light so that you could (or “would be able to”) read. (Best, standard Engllish)
Again, no commas are necessary, and, indeed, would possibly confuse the reader.

3. Actually #3 is OK except that you would say “any noise” or “a sound.”
That’s the way we speak. #3 is understandable, but “a noise” refers to a single outburst, while “not a sound” would suggest a continuum of silence. Apart from that, #3 is OK without the comma. No comma is necessary, and indeed would be confusing. In all three instances you would use a comma if the subordinate clause came first.

I didn’t make a sound so that he would not notice me.
So that he would not noice me, I did not make a sound.
Acutally, “In order that” is more natural in this sentence, but “so that” works.

In all three cases, there might be a better way to say them. The negative can be hard to follow. For example, “I was perfectly silent so that he would not notice me.” Even better in most cases would be direct cause-effect statement such as “I was perfectly silent, so he did not notice me.” That, of course, expresses effect rather than purpose, but in most contexts this is clearer. Also, in this case, “so” is a coordinating conjunction, the clauses are independent, so you use a comma.

I hope this helps.

[Note to our readers. I learned that this question and a number of others from “N” or “NT” are from a non-native English speaker whose native language uses phrase in most cases where English uses clauses. But these clause questions can be helpful to anyone who wants to learn to be more precise.]