He is a fragment of William's soul, however he acts nothing like him. Plushtrap has a few specific memories, not including the murder William commited. He does however have memories of the fazbear frights fire.
Plushtrap isn't aware that he's the fragment of a soul and passes the memories off as weirdly vivid dreams.
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FNaF Headcanons (Mostly Daycare Attendant)
RandomJust some of my FNaF headcanons, nothing special