He was an Unspeakable at the Ministry, and god only knows how he pulled  that off. Following the war, his entire family had been arrested for their crimes. Narcissa was pardoned immediately; having never taken the Dark Mark and given Harry’s testimony of what had transpired in the dark forest. Lucius was sent to Azkaban, and Draco was given a lengthy trial, along with a few other young men involved in the Death Eater cause, including Gregory Goyle and Theodore Nott. The final verdict was not guilty, and they were all acquitted from their crimes. Draco’s release especially caused significant outrage in many wizarding circles. He became a pariah of sorts. Perhaps that’s why he was an Unspeakable; for everyone preferred to hide him in the basement of the Ministry. 