The Nazis actually basically did what you are describing. Beginning in the fall of 1944 the SS began evacuating camps that were close to the approaching Allied army on the western front and the Russians on the eastern front. After the camps were evacuated the sites were destroyed to hide the evidence of their genocide against the Jews.

These forced marches of thousands of prisoners are what are known as the death marches. Some of the time Jewish prisoners were brought to places to be shot and killed en mass. For example as the camps in the Stutthof area were evacuated the prisoners were marched to the Baltic Sea where they were shot. More often the marches were to trains to take the prisoners to other camps farther from the front.

The death marches were brutal. Most occurred during the winter so prisoners were forced to walk dozens of kilometers in the snow without food or water and without stopping to rest. Those who fell down or lagged behind were either shot or left to die.

These marches did succeed in emptying many of the camps. Although Auschwitz-Birkenau at full capacity could hold 100,000 prisoners when the camp was liberated by the Russian army only about 7,000 prisoners were still there. They were the ones too weak to go on the march and had been left there to die by the SS. The camp was also largely destroyed. If you go to Auschwitz today you will see green fields where the barracks and most of the other buildings were. In contrast, the Majdanek camp was liberated fully intact. Although the SS evacuated the camp they did not have time to destroy it before the Russians liberated it.

This map from the US Holocaust Memorial Museum shows the paths of the major death marches.

A college professor once fielded this very same question in class one day and described how the Nazi regime accelerated its genocidal programs as they realized the war was over because they felt a moral obligation to cleanse the world of inferior people. Is this a true assertion by my professor?

As some of the other commentators have pointed out in this thread, there were multiple types of camps and they often had different purposes. The important thing to realize about the Third Reich is that the reality of its governance was far from the popular conception of it as centrally-organized totalitarian state. There was often significant organizational overlap and competing bureaucracies and very frequently the left hand did not know the activities of the right. The SS-run camp system was no more immune to these centrifugal tendencies than the rest of the Third Reich's state apparatus. When the SS began to use its vast number of Jewish and other prisoners as a labor force there were orders to preserve a core of skilled labor for use as slaves in industrial wartime production that coexisted with grueling physical labor such as building underground factories in which the prisoners were worked to death. Although the mass gassing operations (Operation Reinhard) had officially ended in November 1943 and the Germans systematically destroyed the evidence of death camps like Bełżec or Treblinka later that year, mass killing operations continued in places like Auschwitz-II and Majdanek well into the following year.

The advance of Soviet armies into the territory of the Reich and the General Government of Poland precipitated a large-scale collapse in the already chaotic organization of this system. There is some evidence that Himmler wished to preserve the remaining number of Jews under German control as some kind of perverse bargaining chip to use against the Western Allies to ensure his continued political relevance in the postwar order. However, the SS also evacuated some of its specialized equipment for extermination at Auschwitz for Mauthausen, indicating that it still anticipated the need to carry out mass executions. Others evacuations were done to preserve what many had begun to see as a state resource and removed those prisoners still able-bodied to work back in the Reich to help the German war effort in its last gasps. The death marches were a means to prevent the Allies from coming across more evidence of German war crimes. The capture of the nearly intact gas chambers at Majdanek was evidence that the Germans did not want to come to light. Postwar memoirists and contemporary evidence like a note at Auschwitz reading "Chaos; the SS in panic," speak to a near frenzied panic mentality of the SS and other German administrators as the Soviet armies closed in on the Reich.

Evacuation of prisoners within this context was highly arbitrary and often quite brutal. Although there were general orders to evacuate all material in light of the Soviet advance, to what purpose was unclear to those running the evacuation. Thus the evacuation process was chaotic and many of the senior officers of the marches abandoned their posts leaving decisions in the hands of junior officers and NCOs. The net result of this was that these various death marches became even more violent, but also more unpredictable. German guards would execute prisoners for minor infractions, but would also sometimes take bribes for escapees or would themselves abandon their charges in light of the deteriorating war situation. The arrival of the remnant of these death marches into the various KL workcamps in Germany itself overburdened an already collapsing camp infrastructure and epidemics like typhus culled out a large number of survivors.

By Spring 1945 the surviving German prison system was overburdened with the numerous evacuees from the East (and to a lesser extent the West), so much so that a mass execution of surviving prisoners was out of the question for the Germans. Some of the few senior SS leaders that did not abandon their posts began to look out for the future prosecutions. The commandant of Bergen-Belsen, Josef Kramer continually filed requests for more resources to deal with the epidemic of typhus and preserved copies of his requests in his personal papers so he could present himself postwar as a diligent and responsible bureaucrat. Other attempts to cover up wartime misdeeds included killing senior political prisoners or other prominent figures like Dietrich Bonhoeffer who could greatly assist any postwar prosecutions.

So there was no giant overarching schema in the Third Reich to eliminate its last remaining victims, nor could there have been given the chaotic situation as the regime collapsed. But the last days of the Third Reich were no less brutal or murderous to its victims than earlier periods of German hegemony.

Sources

Kershaw, Ian. The End: The Defiance and Destruction of Hitler's Germany, 1944-1945. New York: Penguin Press, 2011.

Longerich, Peter. Heinrich Himmler. Oxford [England]: Oxford University Press, 2012.

Wachsmann, Nikolaus. KL: A History of the Nazi Concentration Camps. New York : Farrar, Straus and Giroux, 2015.

Follow up question, exactly how many were rescued from these camps? I read that allied troops liberated 50-60 000 people from Buchenwald alone.

You have to keep in mind that those people in the concentration camps were not just "prisoners". They were a valuable resource of slave labor. If you take Auschwitz for example, those imprisoned there were the ones that were seen as strong enough to work at the infamous selections. Those deemed "weak" were sent into the gas chambers.

Furthermore at the really last stages of the war it was just a question of time and resources (and of course the unwillingess of most camp guards to get captured red handed). You can't just kill several thousand people in a short time. This is process that needs logistics and planning (See for example Snyders Bloodlands)