When the protagonist sees her, the game will start glitching out and the music will heavily be distorted, playing the song "Sayo-Nara", a distorted version of the menu theme. Regardless of the protagonist's choices prior, he will rush into Sayori's room, where she can be seen hanging by a noose from her neck. Sayori's ending happens halfway through the game.
(Note: This isn't necessarily an ending to the game, but more the events that lead to the end of her life.
Character-Specific Endings Sayori's Ending