This page shows various glitches that can happen in the games.
The Stuck Security System Glitch
This Glitch can happen two ways
1. If either Withered Penguin or Withered RAT restarts your monitor as The Withered Animationic or The Cat attack you it would glitch out the game making it act like you don't die. but while you are like this you can not use the Security system or move. This glitch is great for beating nights.
2. It happens at random, but if you are stuck in the Security system you can still use it.
A glitch that happens when any of the animatronics attack you can result in you not dying and beating the night while being stuck and unable to use anything. This has been fixed presumably.
Unkillable Bed Glitch
There's a bug where when Monster Vinnie is active and you look under the bed he can't kill you. This has been fixed presumably.