If you want to apply forces to your player/monster and don't want it to move, resulting forces in the direction of movement must be zero. It's Newton's second law consequence.
Why don't simply change your player concept and leave it move with friction? If no friction, the the player has to be stopped by user interaction (i.e. a button/action to stop it)
For monster I wouldn't use RigidBody2D, better KinematicBody2D