The Valiant Must Fall Vol. 2 by Yu Aida

SHE WILL KILL HER MOTHER, THEN HERSELF. Shino wants to end her life, but not before ending her mother's, saving them both from a fate worse than death. However, they are Adashino, immortals who can't be slain by ordinary means. That's why she's enlisted her new kinsman, former samurai Haruyasu, to steal a sessho-seki, a blade capable of killing the unkillable. But wielding one also claims the bearer's life. Can Haruyasu help Shino fulfill her duty without sacrificing himself as well?
Binding: Paperback / softback