Every time you die, you respawn right next to Banker - and an empty puppet-case. This heavily implies that the "resurrected" Bandit is merely a brand new one and the one you've been playing up until the point of your death has been Killed Off for Real.
The beginning of the game shows Bandit as clearly sentient and able to move without the strings - until said strings are forcibly attached to him in a manner that doesn't just look unpleasant but downright painful. Bandit is basically in a horrible And I Must Scream situation, with someone neither he nor us can see piloting his body against his will. Worse, it's heavily implied that this is irreversible, as cutting the strings is an automatic Game Over.
Adding on to that, ever wonder why Bandit never speaks in the game, despite clips of the show proving that he is capable of it? Well, the obvious implication is that he can't. Or at least not until the puppeteer lets him.
This makes the other puppets' nonchalant acceptance of the situation even creepier. They all know what's going on with Bandit, yet they let it happen because they either don't care or are too afraid of the consequences if they help him. If they can even help him...
Penny's Eye Scream is creepy enough as is, but it gets worse: we know why she pulled them out, but we have no idea how she removed them. If she did it herself, then did she do it with some kind of tool or did she pull them out with her bare hands? If she got somebody else to do it, then who? Was it somebody we met, like Doc Carver or Miss Undertaker, or somebody we've never seen before?
There's a small coffin in Miss Undertaker's hut that can be interacted with. Doing so will prompt her to state:"Silly Bandit, you can't open that yet." Is she implying she has a coffin already ready and waiting for Bandit? Or is it just her own particular brand of Gallows Humor? Either way, that line is more than a little unnerving.
Dave and Betty's note, which details their escape from the Araknits and their hope that they'll be found before they starve to dea-wait, starve? They're...puppets. Why do puppets need to eat?!?
Fridge Brilliance
Pay close attention to Miss Undertaker in the starting cutscene. When she states that Bandit being where he is must be what "he" wants, she subtly points upwards with her left hand. "He" most likely refers to the puppeteer, so the gesture is a deliberate nod to him.
