Can one personality kill another personality?
Far from being simply encoded in the genes, much of personality is a flexible and dynamic thing (Mischel &amp; Shoda, 1995) that changes over the life span and is shaped by experience (Roberts, Walton, &amp; Viechtbauer, 2006).
  Can Personality Be Changed? by Dweck


After searching for related case studies, this is the closest I could find: "Deathman, age 27, intervened when John, Gail and Diana argued." -- Four Cases of Supposed Multiple Personality Disorder: Evidence of Unjustified Diagnoses This women's multiple personalities fought each other (even though the authors doubt she had MPD). 

Perhaps "kill" is not the best word.