Oliver Messaien wrote his haunting Quartet for the End of Time when he was a prisoner in the Gorlitz concentration camp in 1940. It started as a shorter trio for clarinet, violin, and cello, because there were just those three musical instruments in the camp. He added a piano when he expanded it to an eight-movement quartet, and it was performed in the camp on January 15, 1941.

Of course the camps were not just designed for extermination. Only some camps in Poland were primarily used for mass exterminations, and then only starting in 1942, when the "final solution" was implemented in earnest. Even those were also utilized as labor camps, where the prisoners were worked until they died. "Straw man" arguments like this are commonly used by people who believe that the Holocaust is all a fabrication ("See, this isn't true, so it's all a lie")...but it's generally not a very sound or persuasive logical technique.

Aloha,
Mark