There is no term in existance. The two genres of music are mutually exclusive of each other. Metal revels in sex, drugs, violence and death. Emo on the other had cringes and cries in a corner at such ideas.
It's either Metal or Emo, not both.
You are thinking of PostHardcore, or just plain EMO, you fucking idiot!
Dude: Fuck I love SLAYER!
Emo: Umm...why do they have to sing about such evil things and like it? Why can't Emo "Metal"have some kick ass music like this but without the evil and violence? It makes me want to cry...(whines)
Dude: Because, pussy, there is no such thing! No one in their right mind would even think about that bullshit! Get the fuck out of my McDonalds...
(Kicks the shit out of the emo loser)