Pulp submitted a song to the producers for consideration for Bond 18 (later officially titled Tomorrow Never Dies). The song, like so many others, was “rejected”. But Pulp, being big Bond fans, were undeterred. They simply retitled the song “Tomorrow Never Lies” (which was incidentally the original title of the film until a typing error) and released it on their latest album.
Jon Bon Jovi was asked to submit a song for Bond 18, either by the producers or by David Arnold. Whether he did or not is unknown.