Monika states in Act 3 during her conversation with the player that Sayori's hands are bloody because her hanging did not kill her instantly, having stepped from a chair instead of a higher place, the latter which would have made her death quick and painless. The 'New Game' option will also be replaced with a line of glitched and distorted text, but its functionality remains the same. When the game forcibly brings the players straight back to the menu, the result is Sayori being switched with a scrambled up mess of each of the other character's sprites where she used to be.
The protagonist claims that she is gone forever and suggests that choosing the other option when hearing Sayori's confession would have prevented this. 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