War and Death are two inseparable things, they are always together, so Asa is without her knowing (somehow) the rebirth of the Death Devil.

When Fami said "Anything for my little sister" it was for Asa as she knows her was the Dwath Devil, but didn't tell that she was the oter sister because Yoru cannot know that to whatever motive.

Also, although we saw Yoru killed at least 2 people and Asa killed none, so Fami might be trying to make her kill someone or atleast, make her get in a situation were she is forced to kill someone (Yuko as she was "Too dangerous to be left alive" , Denji as she needed to go out of the aquarium) and maybe by killing someone Asa's "Death Powers" will start to work again. Also ain't weird that she indirectly kills a bunch of people? Her mother, Yuko, Class president and the Teacher.