Can my friend stay in Thailand on a one-year volunteer visa after his work permit expires?

I never heard that you get an extension longer than to the end of your work permit. Very strange

I would bet if your friend actually looked at their stamp they'd see that it is NOT a visa at all but an "extension of stay" 😮

AND that means when the terms to have that extension are no longer met (like cancelling a work permit) they have to go and cancel that extension of stay too

So no they cannot stay until Dec, when their work permit runs out they go cancel their current extension at the immigration office.