I think that there will be different answers based on the different camps to which Eliezer and his family progress. For example, when the family arrives in Auschwitz- Birkenau, the camp features different processes. When Eliezer is separated from his mother and his sister, presumably this purpose was for selection as to who will live and who will die. When Eliezer and his father go to Buna, for example, it is for a work detail and forced labor. The purpose of each camp is different, but all of the camps are designed to oppress those who were deemed as enemies of the Reich. At the time of the narrative, the final solution was the end purpose of the camps that the Nazis controlled. While not all concentration camps were directly intended to be death camps, death was the end purpose for all of those who ended up going to the camps. They were sent to the camps for the purpose of fulfilling the policies of the Nazis, in which death for those who were of the Jewish faith was seen as the ultimate end purpose of all camp processes.