A wallflower: The odd person at a social event/party who stands to the side, fades into the background, as they are too shy to ask someone to dance or no one wants to dance with them; This isn't generally based on the person being appealing in a attractive level.
Though when someone looks through the throng of moving bodies and goes over to this ,presumably, oddity of a person and gets to them they discover they're the most interesting person they have ever met.
“He's a wallflower. You see things. You keep quiet about them. And you understand.” -Stephen Chbosky,The Perks of being a wallflower.