The Purple Man meets Purple Man event was a cloning event in which the Purple Man got cloned before he destroyed the animatronics, and the clone was the one got stuffed. The real Purple Man is still alive while the clone is in Springtrap.
The Purple Man, sitting in his apartment, was cloned by someone hired by Fazbear Corporations in order to get a "good Purple Man" to tell him the events of what happened and his involvement with Freddy's Fazbear Pizzeria and Fredbear's Family Diner. Afterwards, Purple Man wakes up in his apartment, noticing some residue and dirt on him, and he thinks that the animatronics came in his apartment and did something to him. He goes to his closet, makes a Purple Freddy, and swears to destroy the animatronics.
Purple Man, like in the game, starts using his Purple Freddy dummy to destroy the animatronics and then cover his tracks with lawyers and legal processes. At Fazbear Incorpation, "Good" Purple Man starts telling everything, from the murders to the incident. They then tell him to go to Fazbear's Fright, and check out the backstage. He walks towards it, looking at the destroyed animatronics, then he sees the spirits. He gets scared, and hides in the Springtrap suit, where he's accidently stuffed.