Karl Arnold Sr. also know as The Fox is a prolific serial killer and the titular main antagonist of the Criminal Minds episode, The Fox and after became the antihero in Outfoxed.
As a child, Arnold was physically and sexually abused by his father, resulting in him developing a self-hatred. At some point in adulthood, he married a woman named Fay and had two children, Karl Jr. and Sarah. However, Arnold's obsessive-compulsive nature resulted in a divorce, during which Fay won full custody over the children. As a result, Arnold began drinking heavily and became unfocused.
Karl eventually worked as a family psychiatrist and family annihilator. He targeted families he viewed as dysfunctional, stalking them for weeks before attacking when they were supposed to go on vacation. He'd bypass the family alarm systems and kill the famil dog if they had one before abducting the family. He'd keep the family separated for days, during which he would assume the role as head of the household. Eventually, he would bring the family together and ultimately kill them all, starting with the children and ending with the father. Prior to the killings, he would beat the male children and rape the female children. After this, he would take the father's wedding rings as trophies.
The BAU was called to investigate after Karl had murdered eight families, mainly to investigate the disappearances of the Millers and the Crawfords. Karl was found in the basement of the Dunken's house, where he used the Dunken infant as a hostage. Karl eventually released the infant and attempted to flee, but was quickly captured and taken to BAU headquarters. At headquarters, the BAU tricked Karl into confessing his crimes by switching the places of two crime scene photos on the board; Karl couldn't stand anything being out of order, resulting in an outburst and a detailed confession to the murders.
Karl returned in season 5, where he helped the team with a spree-killer case. During the episode, it was revealed that the legendary serial killer know as The Reaper was secretely working with Karl Arnold.