Unpublished games are those designs that either (1) have been presented in public or played in prototype form but don't yet have a publisher attached to them or (2) have release dates that have long since passed, bringing into question whether the game will ever see print. (Ideally in the latter case, we can verify with the publisher whether the game will still be released, but sometimes doing so is difficult.) If a game is available as a "print-and-play" download, BGG considers that game (Web published); if the game has a specific publisher attached to it but is not yet available on the market, technically that game is "unpublished", but BGG prefers to track that information through a game's "released/unreleased" status for a particular version.
To make a correction to an item that is (Unpublished), do not add publisher- or game-specific information to this entry, as it is attached to hundreds of database items. Instead, use the Submit Corrections button in the relevant game entry(-ies). Before you can list a publisher with a game which is not yet in the database, you must first add that publisher at Misc --> Add Publisher.