If a player has no Units at a Battlefield and the turn is in an Open state, they lose Control of that Battlefield in the following cleanup unless there is a Combat or Showdown ongoing there.
§ 190.4.c Core Rules PDF (officieel)
§ 190 Battlefields
§ 190.4 Control is established by having Units at a Battlefield at the end of a Showdown or Combat after applying the contested status.
