In MatPat's newest Game Theory about Five Nights at Freddy's, he concludes that Five Night's at Freddy's 4 has made a huge mistake. It is widely regarded that the child that we play as is the victim of the Bite of '87. Proof exists as MatPat has mentioned, in the form of flowers, pills, and an IV appearing next to the bed. Additionally, we see the Bite of '87 actually happen in the night 5 minigame. Therefore, we are playing as the victim of the bite of '87, and the events of the game happen after the bite.

Now, the Bite of '87 has always been notorious in FNAF lore after Phone guy's mention of the incident in the first game: "But then there was The Bite of '87. Yeah. I-It's amazing that the human body can live without the frontal lobe, you know?" As MatPat indicated in his video, in correlation with what the majority of the fan base has concluded for some time, was that the bite caused the removal of the frontal lobe. Thus, we are playing the game as the child without a frontal lobe, in a coma-esque state filled with terrifying nightmare animatronics. But as MatPat mentions in his video, the removal of the frontal lobe creates symptoms that are quite the opposite of those presented in the game, and in fact, lobotomy has been used in the past to cure patients of exactly what seems to be happening in the game. I feel like MatPat and the fanbase as a whole are overlooking a possibility that would explain why we see the things we do in FNAF 4, and is better supported by the evidence in the Bite of '87 minigame than MatPat's explanation.

The Bite of '87 did not remove the child's frontal lobe. As seen in the minigame, the Bite of 87 was not targeting the frontal lobe at all. When Fredbear bites down, the whole head of the child is damaged. Therefore, I believe that we are playing as the child after the bite, but before the removal of his frontal lobe by the doctors that are trying to save him. His frontal lobe either needed to be removed because of all of the trauma to his brain, or because the doctors were trying to spare him of his terrifying nightmares that we experience in the game. As /u/Kiyanavasala has previously mentioned, two of the most common effects of brain trauma are "Anxiety For example, panic attacks, nightmares, and feelings of insecurity)" and Obsessionality (obsessive patterns of behaviour such as washing or checking things)". Both of these are profoundly tied to FNAF 4. Once again, MatPat says himself in his video, the removal of the frontal lobe has been used in the past to cure patients of these symptoms. Did the doctors remove the child's frontal lobe because they felt sorry for this child, coming in and out of consciousness screaming for their life? Or was it simply a medical necessity to try to save the child's life? I don't think that we'll ever know the specifics of the operation, but FNAF fans can rest easy knowing Scott wasn't being careless in his making of the game.

TL;DR: The Bite of '87 did not result in an animatronic biting off a child's frontal lobe. Instead the Bite caused brain trauma which led to doctors eventually surgically removing it. The game takes place while the child is in the hospital, in the time between the Bite and the eventual removal of his frontal lobe.