The character models are mounted on bases. However, the character themselves do not remain motionless. They have distinct idle animation which reflects the dark and grotesque atmosphere of the game. When they take action they remain attached to their bases (or not if they don't have such) but their bodies interact with the surroundings, for example, they clash with the enemy or react to falling. The animation looks like your favorite stop motion pictures which emphasize the tabletop and turn-based aspect of the game.
Image Copyrights: Corpse Bride - Behind the scenes, Pinterest