(written from a Production point of view)
Referenced in the second draft script of the Star Trek: The Next Generation episode "The Inner Light", Starbase 243 was a Federation starbase to which the USS Enterprise-D was en route when it first encountered the Kataan probe. In the script, the facility's name was formatted "Starbase Two-Four-Three".
In the final draft of the episode's script, this line was changed to instead reference Starbase 218.  By the time the episode was finalized, all mention of such a starbase was removed from the episode entirely.