Carlos Ribas put it off as long as he could. He had no interest in the government handouts, the holiday cash bonuses, the dirt-cheap groceries, the discounted medical care, none of it.

Then President Nicolas Maduro declared that Venezuela’s extraordinary subsidies for gasoline and motor oil will soon be available only to holders of the Carnet de la Patria—the Card of the Fatherland. Everyone else will pay “international prices” for what has long been the cheapest petroleum in the...