It turns out that the last priest is not the last priest. In the wake of our protagonist's execution, a priest arrives at the home of the faithful mother and is let inside by the once skeptical boy. He's about to tell the boy his name when the youth kisses his hand. And so another nameless priest has come, presumably with his own struggles, but facing the same dangers. Like the Energizer Bunny, the Church keeps going and going.
Greene is hinting at the traditional Catholic understanding of the Church. For the faithful, the Church is a human institution, and in that sense fallible, but it is also a divine and eternal institution. The Church exists beyond death. The saints are as much members of the Church as the living are. With this in mind, Greene is standing athwart the history of anti-clericalism, yelling, "Look, guys, this persecution just isn't going to work out for you. Sorry."