It might work - it has worked for others before. But nothing is for sure - especially not at the moment.

Basically each stay can be extended by 30 days. So she could go to immigration and ask for an extension. They might give her that. She would then most likely have to pay for the overstay (500 Baht per day). Or she could try to find a plane and leave ASAP and pay for the overstay at the airport.

US citizens apparently also received such a letter from their embassy and they were able to get an extension by showing the letter together with the email addressed to them from the embassy. So you could try it that way. Just scroll up a bit in this post and you can find.

Austria apparently issues the letter as well.

1

Trial and Error...

Hi,

You can get the extension at the immigration office where you’re registered. If you stayed in a hotel in Jomtien they probably did the TM30 report. In that case, yes, you can do it in Jomtien. If you stayed private, make sure the ™30 has been filed.

I read, that Jomtien often asks people to come back 3 days before the expiry date of the current stamp if they are busy. Just be prepared for that or plan accordingly.

Actually depending on the immigration office your housemaster (that could also be you) would have to file a TM30 within 24 hours. I think I remember from Bangkok, that they could give you a hard time when you go for your next extension of stay and this notification was not done.

Yes, 90 days start to count again from your entry date.

Basically the only real benefit of the yellow book is, that you always have a "certificate of residence" on hand. This is necessary when you buy / sell a vehicle, apply for / extend your driving license, open a bank account and that's about it.

Getting it depends on the Amphur and mostly requires documents such as birth certificate (translated), passport (translated), 2 Thai witnesses and more...

Regardless of what happened, you can still make your appointment tomorrow. Book a plane ticket for tomorrow early morning to Udon Thani. Make sure to arrive around 7am. The ticket will cost your around 1200 Baht. Then take a taxi or van from the airport to the border and cross over to Laos. You will still make it in time.