I just read Primo Levi's "If this is a man" and he talks about how it was actually a plus to get certain diseases, because you could rest in the infirmaries for a while. This brings up the question - Why didn't the Nazis send all the sick people at Auschwitz to the gas chamber? Why have infirmaries at all? Thanks!
I'm a licensed tour guide at the Sachsenhausen Concentration Camp Memorial. Not Auschwitz, but the general policy for the infirmaries was the same throughout the concentration camp system.
The purpose of the concentration camp infirmaries was multi-faceted, and they were used both as sites of convalescence and healing, as well as murder and torture.
The SS doctors who ran the infirmaries were often poorly trained or not very well qualified (a notable exception being Mengele, who was a respected figure in his field at the time), and in any case had little to no interest in treating ill or weak prisoners. The day-to-day seeing of patients was actually done by prisoner-doctors. In many concentration camps (certainly in Sachsenhausen), for a number of years it was strictly forbidden for any prisoner who had actually been a doctor to work in the infirmary as a prisoner-doctor. This meant that the "prisoner-doctors" often had absolutely no clue what they were doing. In Sachsenhausen and throughout the concentration camp system that policy would change in 1942, when the war was turning against Germany and the slave labour was suddenly not as disposable as it had once been. From 1942, prisoners who had been doctors before their lives in the camp (often much more competent and qualified than the SS doctors) were allowed to work in the infirmary. They had to tread a fine line between helping prisoners to survive and not being seen by the SS to be too soft on other prisoners, keeping them in the infirmary when they could be out doing slave labour. Even after 1942, the level of medical care was nowhere near adequate and the shelves were rarely stocked with enough essential medicines. Furthermore, in the second half of the war the camps became increasingly overcrowded, compounding the problems of unhygienic conditions, malnutrition and debilitating slave labour which caused the disease and illness within the camp to ratchet upwards. At this point, even if the SS had wanted to give proper medical care to all the prisoners (which they did not), it would have been very difficult to do so. The best care generally went to well-connected prisoners within the camp hierarchy, i.e. the Kapos who ran the camp. As Primo Levi mentioned, many prisoners did not necessarily want to go into the infirmary to get adequate medical care, but to get out of doing a day's slave labour - which could be life-saving.
The infirmaries also had a propaganda purpose for the Nazis, who would occasionally allow visitors into the camps, either from Axis nations or even from neutral or enemy countries. They would often carry out staged tours for visitors in which they would be led to select areas of the camp. The infirmary could be used to try to prove that, actually, these camps were "normal" places of detention where inmates could receive medical care.
The SS doctors were perhaps more likely to kill patients than they were to help them. As the camps became increasingly overcrowded, they became full with Muselmänner (the concentration camp slang for prisoners so ill and weak that they were no longer really human anymore but walking skeletons. The translation is "Muslims," apparently in reference to the fact that hunched-over, crawling prisoners resembled Muslims at prayer). Heinrich Himmler's solution was Action 14f13, a program to murder prisoners that were, in Himmler's words, "excess ballast." In other words no longer able to work because of the debilitating conditions within the camps. This operation began in 1941, originally carried out by the same doctors who had been murdering mentally ill and disabled Germans during Action T4. Later the Camp SS doctors carried on this procedure of their own initiative, murdering primarily through lethal injection.
The infirmaries were places of quarantine when deadly diseases broke out, e.g. typhus, tuberculosis, and other diseases which could affect not just the prisoners, but the SS guards as well. Often prisoners were shut away in a certain wing of the infirmary (although sometimes they were locked in a few specific barracks within the camp) and left there to die.
The infirmary would also be used by the SS to carry out gruesome medical experiments on human beings. They were additionally used to castrate homosexual prisoners.
To answer the question of "why didn't the Nazis send all the sick people at Auschwitz to the gas chamber?" The fact is that often they did. The SS would sometimes go to the infirmary and select every prisoner that was no longer capable of work and send them to their deaths. But policy fluctuated with the changing circumstances of war and the various (often contradictory) policy goals of leading figures in the SS, e.g. Himmler, Oswald Pohl, Theodor Eicke. Sometimes they were more worried about preserving their labour force, or at least keeping them alive to get just a bit more labour out of them. Sometimes they were even thinking about perhaps retaining some prisoners so they could hold them as hostages to make some sort of deal with the Allies. The fate of the prisoners inside the infirmary often depended on events that were taking place far outside of the infirmary's walls.
The best book about the concentration camp system, and one which spends a good deal of time talking about the infirmaries, is Nicholaus Wachsmann's "KL: A History of the Nazi Concentration Camps." It just came out this year and I really can't recommend it highly enough. A more Sachsenhausen-specific source (not what you're asking for but where I've gotten some of my information for this post) is "Medical Care and Crime: The Infirmary at Sachsenhausen Concentration Camp" by Günter Morsch and Astrid Ley.
The same question was asked a few months ago where I answered the question.
https://www.reddit.com/r/AskHistorians/comments/31hpm2/why_did_auschwitz_have_infirmaries/