The dirt poor won't see a penny.
When I rented and the property taxes went up, my rent went up to cover the property taxes. The landlord never paid.
If the gas tax is passed on to corporations, they'll find a way to recoup it from the end users, no matter how poor they are.
Please see ER's suggestion and my reply, above. And TB's reply too. There's caring, and then there's caring. One kind seeks to help, and the other, to help one's self.