The Possessor is quite weak on its own, but is able to animate the various statues and sculptures around the castle. In this manner, it can become the Thresholder, as well as a Gargoyle Knight or Warrior.
 Kingdom Hearts 358/2 Days
Roxas experiences a memory of Sora fighting Possessors in the Rabbit Hole section of Wonderland during Mission 47, even though Sora did not fight Possessors until Kingdom Hearts II, which shows the connection between Sora and Roxas revealing itself.
 Kingdom Hearts II
The Possessor possessed the Dungeon doors in the Undercroft, transforming them into the Thresholder in order to fight Sora. After being forced out of the doors, it floats about helplessly before returning to them, reanimating Thresholder. Though it summoned many Hook Bats, Gargoyle Knights, and Gargoyle Warriors to assist it, Sora, Donald, and Goofy were able to vanquish the Possessor, returning the Thresholder into a normal door as the Possessor faded into darkness.
Other Possessors animate the Gargoyle Knight and Gargoyle Warrior Heartless and appear when they are destroyed, but disappear without attacking Sora. The Dark Thorn can summon Possessors to throw at Sora, but these disappear as soon as they are thrown.
The Possessor is a simple, gaseous creature that bears some resemblance to the Darkball Heartless, sporting a similar, jagged mouth—albeit the Possessor's is red—and glowing, yellow eyes. It is seemingly made up of black and dark blue and purple shadows.
The Thresholder is made up of two ornate statues carved into a grey, hexagonal doorway. Each statue has one arm "trapped" in the door, though their claws are seemingly grasping the gold lock in the center of the door from the other side. Each statue on the Thresholder takes the form of a muscular, black-skinned demon with a thin, jagged mouth, spherical head, and beady, glowing yellow eyes, similar to a typical Heartless. Its chest, exposed arm, and each of its short, pyramidal horns sport a jagged, yellow pattern decorating them. Each wears a green collar with four short, silver spikes on it, and their hands end in three red claws. Their backs are lined by short spikes, and their lower bodies are actually curled, interweaving tails with yellow tips. Their lower and upper bodies are divided by a thick, sky blue "belt".
In Kingdom Hearts II Final Mix, their appearance drastically changed, the Thresholder statues have lilac bodies, while their horns, head, arms, belts, and chests are dark indigo. Their claws are yellow and their collars are now violet. The door is now black and the lock is cyan.
The Possessor's name clearly refers to its ability to take control of inanimate objects. The Thresholder's name comes from the word "threshold", which has a variety of meanings, one of which is "an entrance", referring to the Thresholder's true nature as a door. Its Japanese name, Gate Guardian, holds a similar meaning. "Gate" can be taken to mean "door" and “guardian" literally means "one who guards", and the Thresholder "guards" the way to the dungeon.
 Kingdom Hearts 358/2 Days
In Kingdom Hearts 358/2 Days, as long as Roxas is touching them, his health will be continuously depleted. Jumping or performing Dodge Roll will help Roxas escape its capture. Its 'attack' is nil-based, so having Nothing to Fear equipped will prevent Roxas from taking damage.
 Kingdom Hearts II
When you first enter the Undercroft, you will encounter Gargoyle Knights. After they are defeated, move towards the Thresholder. Hook Bats will arrive to defend it. After you defeat a second wave of Hook Bats you are clear to attack Thresholder. The Thresholder will attack by extending its arms across the room and summoning orbs of darkness, so try to avoid those. When his health depletes to a certain point, you can now use the unlock reaction command to release Possessor from the door. Possessor has no form of attack whatsoever, so you're free to go on the offensive.
Eventually it will float back to the door and reanimate it. Thresholder then starts to shoot projectiles at you. Move in close to attack Thresholder without being hit. After you deplete its health again, Possessor comes out and floats around again. Eventually, it will extend its arms at full length, cross them over, and continuously slap you. When its health is gone, you have defeated both bosses. If Sora dies in this fight, The King is temporarily playable.
 Notes and references