Pigley is Krieger's project. Dr. Krieger is known to do many unorthodox projects on ISIS's dime, and Pigley is one of those. Not much is known about the previous Pigleys. The current Pigley, Pigley III, was shown in "The Honeymooners" as what appeared to be a normal pig, just heavily irradiated. He also seems to enjoy eating human flesh.
Pigley is first mentioned in "Stage Two" as a half-human, half-pig hybrid, who is never shown on screen. In a flashback, Krieger is shown having to put down Pigley whilst saying: "That'll do Pigley, that'll do."
Pigley was shown pig experimented on by Krieger in "The Honeymooners", and possibly having a plutonium rod in his rectum, also Krieger's. Pigley glowed bright green, as if he had already been strongly irradiated. It is unsure if the plutonium rod is what Krieger was smuggling to the North Koreans, or if it was part of creating Pigley. At any rate, Pigley enjoys eating human flesh, which Krieger consents to, telling Pigley "God knows you've earned it".