Jason was killed by the Regulators in Adytum. Their motivation to do so was to have a reason to rid the Boneyard of the gangs, most namely, the Blades. One night, Jason was trying to sneak into town to see his father, but the Regulators killed him, and placed his head on a stake for Jon to see. Razor is in possession of a holodisk that shows the conversation between two regulators prior to Jason's death, and the truth about the situation.
Jason Zimmerman does not appear in any Fallout game. He was supposed to appear in Fallout, but was cut from the final version of the game, for unknown reasons. His dialogue file can still be found in master.dat, though it is unused.