In a multiplayer game, if the protector of a battle leaves the game and that battle is not currently being attacked, its controller chooses a new protector for it as a state-based action. If it is being attacked, its controller chooses a new protector for it once no creatures are attacking it. This means that it continues to be attacked and can be dealt combat damage as normal.
Invasion of Kaldheim // Pyre of the World Tree
A Siege’s controller can’t be its protector. If a Siege’s protector ever gains control of it, they choose a new player to be its protector. This is a state-based action.
Battles can’t attack or block, even if one also becomes a creature. If an attacking or blocking creature somehow becomes a battle in addition to being a creature, it is removed from combat.
Magic: The Gathering · ™ & © Wizards of the Coast · Illus. Bryan Sola
Card data via Scryfall. Rarix is fan-made; not endorsed by the rights holders.
