Deaths occur in the Five Nights at Wario's games when an enemy has entered the player's room and the player does no attempt to fend them off. Shortly, the enemy will jumpscare the player, killing the player in-game, leading to a game over screen.
In Five Nights at Wario's, it happens when both doors and lights have been jammed by either Wario, Waluigi, Luigi, or Peach, or the player runs out of power, or Mario gets inside your office and you do not pull up the Monitor. The death animations are the specific characters leaping at the player's face. In the game over screen, Waluigi can be seen with the night guard's head in his hand.
Oddly enough, if an enemy is at the player's door, it is possible, albeit unlikely, that the enemy might leave the door and go back to a previous room, instead of entering the room to jumpscare the player. This could be a glitch.
In Five Nights at Wario's 2, it happens when an enemy enters The Office and the player does not hide in the Backroom or if you fail to keep checking the Tool Storage and Toad sneaks into the office. While hiding in the Backroom, the player must not charge the Generator until the enemy leaves, or they will be attacked anyway. Also, if the generator goes out while you're hiding from a ghost, you'll eventually get killed after a few seconds whether you touch the generator or not. The game over screen features Wario in the Studio with blood on his mouth.
In Five Nights at Wario's 3, it happens when an enemy is left in the room with the player for too long. Even so, the various room mechanics in the game may not make this completely true. The game over screen in this game is merely a black screen with the words "Game Over".