But why wouldn’t they keep looking for the Best Pilot in the Resistance and the traitor that knows about their entirely secret Starkiller Base? I think a squad of 8-14 soldiers in TIEs and perhaps a shuttle would find both people quite handily, especially since life detection equipment was in use in ANH and ESB by the Rebellion and Empire.
Since Poe says he was thrown from the crash, it makes it sound like he didn’t eject.