Q: Is this structure being used in English: "Can you be free not to do something"? On an Instagram page, I heard of a structure being used when you actually ask someone not to do something. The structure was: "Can you be free not to Infinitive...?"
For example:

Can you be free not to nag a lot?

I know that he meant to transfer the concept of:

Would you please not nag a lot?

But I searched on the web and couldn't find any such structure, and as these guys have had a few mistakes in their lessons before I thought here would be the best place to ask.

A: Can you be free not to X is a grammatical but rather unlikely way of saying "Do you have the freedom not to X?", or more directly "Are you compelled to X"?
It is a question not a request, and I cannot imagine a context in which it will be interpreted as "Please will you not X".

A: Technically it is correct. It does sound awkward, though.
Should you wish to be cute, you might try this:
"Would it be too much of a burden for you to stop nagging?"
