How does death affect population change?

Death in and of itself may or may not affect population change.  Population growth, loss, and stagnation are functions of tallying up births and deaths worldwide.  If we are inquiring about population change in a particular country or continent, then we must also include immigration and emigration in the calculation.  
If the number of births equals the number of deaths and there is no immigration or emigration, population remains the same.  If immigration and emigration are equal, the same is true.  Population increases when there is more birth than death and/or more immigration than emigration. 
Over the course of history, there have been many ebbs and flows in these factors.  For example, the bubonic plague is said to have wiped out approximately one third of the population of Europe. Smallpox was a major killer, too.  Cholera and Ebola are two other diseases that have the capability of reducing a population dramatically.  Some countries have very high infant mortality rates for a number of reasons, with not enough increase in births to compensate. But China was so concerned about its population growth that it instituted a "one child" policy for many years to suppress the birth rate.  Australia's population, aside from its aboriginal peoples, began with immigrants from Great Britain, as did enormous swathes of Canada. Today, we are witnessing mass migration from Africa and the Middle East because of war, hunger, and instability, mostly to Europe, but also to other parts of the world.  The population increases in some European countries is dramatic. 
So, we must remember that death alone is not responsible for population growth or reduction. It is a combination of factors, death, birth, and the movement of people.
https://www.history.com/topics/middle-ages/black-death