Where you want to hug someone who could possibly snap and murder you.
They are a physco, a murder, a cold hearted killer or so you'd think until you looked into their backstory. Turns out they have a heart and it's burried somewhere under that tragic past. Their past alone is a tear jerker that makes your want to reach into the screen and give them a hug. Their present selves makes you want to do the same.
Examples: Soul Eater's Chrona. Naruto's Gaara.