So, interesting and maybe-not-so-fun fact? Most parasites that kill their hosts do so without caring because they can survive elsewhere. We call it a reservoir of infection.

REALLY fun fact, there's some cool life cycles involved. You remember our old friend anthrax? One of its favorite tricks is killing its host, the zebra. When it dies, the anthrax bacteria go down into the soil beneath the corpse, and put on a fresh new coat of paint and open up shop again. Only, this time, they act as a super friendly bacteria that participates in the nitrogen cycle and ensure that the plants in the soil can get everything they'd ever want out of that oh-so-convenient zebra corpse rotting away up above. Why do they do this? Because in their 'friendly' infection of the plants growing (oh, did I forget to mention what plants they infect/cooperate with? It's grass), they get offered right up to the hungry mouths of the next zebra to come along and see an exceptionally vibrant area of green grass.