I have a stupidly complicated theory about the Purple Man. I'll just copypasta it from the FNAF wikia's forum, where I originally posted it.
I have a theory: Fritz Smith is the killer behind the Missing Children incident, and the Purple Man is the killer. For this to work, I assume: Fritz was a daytime employee, Phone Guy covered the player's shift on night 7, which was not a Custom Night, and the Custom Night never happened in-universe.
At the beginning of this theory, we have the "give cake" minigame. The important part is that The Purple Man (Fritz Smith) kills a child, outside of the restaurant.
Then, in the minigame where Freddy chases the puppet, Fritz/Purple Man sometimes makes an appearance, chasing Freddy and ending the game if Freddy is caught. The game ends with a blue screen, as if Freddy crashed like a blue-screened computer; this depicts the incident Fritz was fired for, tampering with the equipment by modifying the Golden Freddy animatronic to create a wearable suit. Golden Freddy is moved to the back room for future repair.
Phone Guy's call on night 3 mentions a "local story" that has "nothing to do with our establishment". He's talking about the murder in the cake minigame, in which Fritz is now a person of interest.
On night 4, Phone Guy mentions that the animatronics are behaving strangely around adults during the day. The minigame that depicts the Purple Man capturing Freddy probably took place during the day prior to night 4, because Fritz only worked one day according to his pink slip. The animatronics were staring at "adult staff"; likely, they were keeping an eye on Fritz because he was now a suspect in the cake murder, which they knew because they are tied to criminal databases. This could have to do with why Fritz modified/destroyed Golden Freddy.
On night 5, Phone Guy mentions that the building is on lockdown, especially concerning "former employees" (Fritz) and that there is an investigation going on (the cake murder).
On night 6, the story ends: Fritz uses the golden Freddy Fazbear suit that he was fired for creating as a disguise to kill four children, which went on to haunt Foxy, Bonnie, Chica and normal Freddy; the killer himself inhabits Golden Freddy in the original game.
So, from beginning to end, we have:
Fritz kills a child prior to working at Freddy's. The day of night 4, Fritz works his only day and is fired for turning the Golden Freddy animatronic into a wearable suit. On night 5, Fritz has gone from suspect to wanted criminal, and the pizzeria becomes related to the case, thus the lockdown and the warning about previous employees. Prior to night 6, the strange goings-on during the player's shift have been mundane software glitches. The day of night 6, the murder takes place: Fritz uses his Golden Freddy suit to kill a number of children, prompting the closure of the restaurant and beginning the haunting of the animatronics. This also explains their extreme aggression on night 6 and the sudden introduction of Golden Freddy.
This theory has its own holes (it doesn't explain GIVE LIFE and leaves a number of questions about the Puppet's behavior), but I think it adds more than it takes away, mostly by giving an identity to the Purple Man.