That's rough. I'm sorry all this has happened to you.
Sadly, there's nothing you can do. Just wait until you get the extension letter by mail and then mail it to her to Japan through FedEx.
You should receive it within 30 to 45 days. She will be able to return to the US with her green card and that letter.
Before buying flight tickets, the first thing you should always do is check if your passport or green card is expired.
For the I-751, USCIS sent me a reminder letter 120 days before the expiration of the green card. I got one through mail and through my online account.