Can my husband extend his stay in Thailand beyond the expiration date of his METV?

Yes

okay, the way a 6 month METV works is it's valid for 6 months from the date it's issued, it's good for unlimited entries during that time, each entry is for 60 days (even if you enter the last day the visa is valid for you get stamped in for 60 days) and you can extend each entry once for 30 days at the immigration office

So the answer to your question are, yes he can get a new 60 day stamp and yes he can get a 30 day extension on that last entry