In 1986 John Hackleman opened a gym he named The Pit. That led to fighters who operated from this base being called pit fighters. The most renowned of those early pit fighters was Chuck Liddell, a martial artist who went on to become the UFC light-heavyweight champion.
Looking farther back in history, however, one comes across the term "pit fighting" in reference to a hard form of Hawaiian kempo — which at one time was known as kajukenbo, yet another hybrid martial art originating in Hawaii in the late 1940s. The name kajukenbo, of course, is formed from the first letters of the names of the arts that constitute it: karate, judo, jujitsu, kenpo and boxing. Not a bad mix at all!