From the MLBUM
7.8 PENALTY FOR BALK..............A runner who misses the first base to which he is advancing and who is called out on appeal
shall be considered as having advanced one base for the purpose of this rule................................
So the result is, if a proper appeal is made, the BR is out as in any other situation and the run is removed. The balk was satisfied when the BR was assumed safe by the umpire when he passed 1st base.