Manic depressive pixie dream girl
A manic pixie dream girl that is broken or jaded in some way and often has a tragic backstory usually suffers some form of mental illness usually a personality, mood, or dissociative disorder and/or ptsd due to/from a traumatic event in her past
Examples of the manic depressive pixie dream girl would be ophelia from hamlet or misaki nakahara from the anime adaptation of welcome to the nhk