Spoiler Alert:
In "Mockingjay," the third book in the Hunger Games trilogy, Katniss does not die in the traditional sense. She does suffer a serious injury, however. She is shot in the head by an arrow, but she survives thanks to a miraculous rescue and medical attention.
The lasting effects of this injury, though, are significant. Katniss experiences trauma and PTSD, and her mental health is forever altered. She is left deeply scarred, both physically and emotionally, from the war and her experiences.
So, while Katniss technically doesn't die in the third book, she does experience a near-death experience and suffers profound consequences from the event.