Pigface was formed from Ministry's The Mind is a Terrible Thing to Taste tour, which produced the In Case You Didn't Feel Like Showing Up live album and video. For the tour, Al Jourgensen brought Atkins, Nivek Ogre and Chris Connelly. Also on the tour was Rieflin, regular Ministry drummer at the time. While Atkins enjoyed the dynamic of playing with a second drummer, he felt that the lineup was capable of doing much more than being, what he has frequently called, "a Ministry cover band." Once the tour was over, Atkins and Rieflin decided to continue working together and recruited several of their tourmates. Pigface was born with the intention of keeping a revolving-door style collaboration with many experimentally-minded musicians, many of whom, especially early on, had recorded for the influential industrial music record label Wax Trax!.

Source

Source

Source
Trent Reznor was also an early partner, before Nine Inch Nails became a household name. "Suck," co-written and sung by Reznor, was something of an underground hit, and Reznor later re-recorded the song for the Broken EP.
Source