At some point, the real Groves was possessed by a demon, presumably to use the resources of the FBI to get at the Winchesters. Agent Victor Henriksen reported to what he believed was Groves, but was actually the demon possessing him. At an unknown point, the real Groves died of an unknown cause though the demon continued to possess his body.
After Henriksen captured the Winchesters on a tip from Bela Talbot, he alerted "Groves" who came to personally deal with the Winchesters. Possessing Groves, the demon was able to get close enough to wound Dean before Sam started an exorcism. Rather than allow himself to get exorcised, the demon fled Groves' body through a vent, leaving Groves dead on the floor. Though Groves' body showed no signs of gunshot wounds, Henriksen refused to believe the Winchesters insistence that they hadn't killed him and that Groves had likely been dead for a while.
The next day, Groves was one of the victims of the "gas explosion" listed on the news report the Winchesters saw.