There was a unit under the control of the the Waffen-SS called the Dirlewanger Brigade (SS-Sonderformation Dirlewanger) that was composed of criminals whom the Nazis were more than happy to get rid of by sending them into dangerous operations they were unlikely to survive. It was led by SS-Oberführer Oskar Dirlewanger, who had himself been convicted of numerous sex and alcohol-related offenses. The original members of the units were people convicted of poaching, but it quickly lost that character as violent criminals, people acquitted of violent crimes by reason of insanity, and political prisoners were added to the unit. There was some controversy around the creation of this unit since it was a group of criminals within what was supposed to be the elite Nazi paramilitary force, although the unit was technically subordinate to the SS, rather than part of it.

When it was established in 1940, it was initially sent to Poland to combat partisans, which was understood to be a dangerous task that frequently resulted in high casualties. In 1942, it was sent to Belarus, where it carried out massacres of civilians, frequently by locking them in a barn or other building and setting it on fire. The unit was expanded into a regiment during this time with the addition of many political prisoners, increasing its numbers to about 700. It was sent to the front in late 1943 as the Red Army pushed the Germans back out of Belarus and lost well over half of its men, since they weren't properly trained soldiers.

In 1944, the unit carried out the actions it's most infamous for. During the Warsaw Uprising in 1944, the Dirlewanger Brigade massacred tens of thousands of Poles in the Wola district of Warsaw, without concern for whether they were combatants or civilians; they may have killed as many as 40,000 people in two weeks. The unit suffered heavy casualties in the fighting during the Warsaw Uprising, and had to be replenished several times. In fall 1944, it was elevated to brigade status and reached its maximum strength of 4,000 men. After the Warsaw Uprising, it was sent to Slovakia to help suppress the Slovak National Uprising, and then to the front lines in Hungary at the end of 1944. In early 1945, it was transferred north to the Polish front and designated as a proper division (the 36. SS-Waffen-Grenadier-Division). Most of the unit was wiped out by the Soviets in 1945, with only about 700 men surviving and reaching Allied captivity. Dirlewanger himself died in Allied captivity in June 1945, allegedly murdered by Polish soldiers.

Source: Hans-Peter Klausch, Antifaschisten in SS-Uniform: Schicksal und Widerstand der deutschen politischen KZ-Häftlinge, Zuchthaus- und Wehrmachtstrafgefangenen in der SS-Sonderformation Dirlewanger (Bremen: Temmen, 1993)