In a longer term sense. If all the viable hosts die day one the virus stops having anyplace to go.
The plague also largely died out after killing a massive portion of the population, if they hadn't been killed it could have gone on for far longer.
Killing the host isn't beneficial for the parasite using it for resources. Not that there's an active effort to be choose the traits, but something that happens to evolve to be less lethal and more easily transmitted will tend to exist longer.