For years now people have wondered why the paperpal ends up in the office, some just think it's a random easter egg that might happen, or that Withered Chica somehow brings it there. In actuality, the paperpal is its own animatronic that has an ai level and moves like the other animatronics.

First off, its AI level. On every night, its AI is set to (Random(100) 1)/100. This means that there's only a 1% chance of it having an AI that is high enough for it to move, and even then it will only have an AI of 1. Also, this can only happen on Night 7, as there is code that sets all AI levels to 0 on nights other than 7. (The order is hard to figure out, comment if you know which is executed first).

Now for how the paperplate actually moves. Every 5 seconds, the game picks a number between 1 and 20. If this number is less than or equal to the paperplates AI, it will set value A to 1. Once value A is 1 and the player is not viewing the paperplate, value A will be set to 2. When value A is 2, the paperplate will move into your office as soon as you are watching any camera except CAM 4. However, it will only be visible when no other animatronics are in the office, presumeably to make it not overlap them.

Interestingly, there is a stun timer for if the player has recently lit the flashlight on the paperplate, as is with other animatronics. This is what value B is used for, and the paperplate can't move if it is more than 0. If the player is viewing the paperplate on the cameras and uses the flashlight, value B is set to "stun time" - night*50. This value is subtracted every tick. "stun time" is a variable that is set to 400. This means that if you shine your light at the paperplate, it won't be able to move for 0.5 seconds

The animatronics that can be stunned like this are the following: Withered Freddy, Withered Bonnie, Withered Chica, Toy Bonnie, Toy Chica, Toy Freddy, Mangle, Paperplate. However, only paperplate subtracts the night multiplied by 50 from the stun time variable, meaning that the stun time is always 4 seconds. Some animatronics, like Withered Freddy, also get stunned for 4 seconds specifically if you shine your light at him in the hallway. I haven't checked all of them but the animationics that don't use the stun time variable might just have a set value of 400 as stun time. Not all of them have the same time though, the puppet for example has a stun time of 10, very short.