I remember very clearly reading a science fiction short story years ago that is EXTREMELY reminiscent of the plot of "Wool". I would really appreciate anyone who can identify it, because with what little I know I can find nothing on the Internet.
The older story is also set post-apocalypse. For an unknown period of time, human beings have been confined to an underground environment known as "Festive" (revealed during the story to be a corruption of "Fallout Shelter Five". The story centers on the fact that to keep control, the authorities tell everyone that the air outside the shelter is poisoned. There is an old man in the story at the top of the shelter who keeps pigeons, and everyone thinks he is crazy for exposing himself for short periods to the poisonous air, but he tells them that he is so old that it doesn't matter to him any more. A younger man is inspired by the old man and at the end of the story opens the main airlock and breathes - and the air is no longer poisonous, and (by implication) everybody can leave.