Public Execution

• WWizards of the Coast2012-07-01
  Official Ruling
  Public Execution targets only the creature it destroys. If that creature is an illegal target when Public Execution tries to resolve, it won't resolve and none of its effects will happen. No creature will get -2/-0.
• WWizards of the Coast2012-07-01
  Official Ruling
  Only creatures controlled by the player when Public Execution resolves will get -2/-0. Creatures that enter under that player's control or that the player gains control of later in the turn are unaffected.
• WWizards of the Coast2013-07-01
  Official Ruling
  If the target creature regenerates or has indestructible, each other creature controlled by that creature's controller will still get -2/-0.

Rulings via Scryfall