I am not an attorney or a financial advisor.
https://www.uscis.gov/sites/default/files/document/forms/i-407instr.pdf
> Include all Permanent Resident Cards, reentry permits, and/ or refugee travel documents in your possession when submitting your Form I-407.
If you give them your PR card, you won't have anything on you to prove your status here in the United States. That seems like a Bad Idea. You do that, something happens before you leave, and you have no easy way to prove you're here legally. You might very well be legal, but why take a chance?
> Form I-407 is used by lawful permanent residents who are outside the United States or at a Port of Entry who want to abandon their LPR status.
That suggests you wouldn't file it while still here in the United States. As an alternative:
> You may also submit Form I-407 to a U.S. Customs and Border Protection officer at a U.S. port of entry.
I have no idea what the practicality is of handing it to them on the way out of the country. (The stories I hear on this board are from people who are trying to enter the U.S. with an out-of-status PR card.)
I'd argue that if you submitted the form, your PR card, and anything else "in your possession" as soon as practical *after* you left the United States, you are legal for whatever reasons you need to be. I might try the port of "entry" that you're departing from just because they'd know what an I-407 is and what to do with it.
Keep copies of everything just in case. Stuff gets lost.
Regards,
Vicky's Mom