(In SG, they are not siblings btw.) Lore on SG Chara and how she ended up underground: The necklace she has was given to her by her mother, who died in the Human/Monster war. She sacrificed her life, so she and her dad can escape, they hide pretty far out, and her father passed from the wounds he sustained in the battle. Wracked with grief, Chara goes to take her life. She survives the fall and meets up with Papyrus. After escaping the ruins, he sees a shivering figure. She gave him the scarf, and the figure turns out to be Asriel. Asriel had a jacket, which was a gift from Asgore. It was too big for him, so he gave it to Chara. Chara moves in Snowdin, and she starts to develop a small crush on Asriel.
also chasriel is canon.