The Billie Jean that Mike was referring to in the song was a woman who sent him letters saying that he was the father of her son (or twins--I forget which exactly). She sent him pictures of them with her as well. He put a picture on display at Hayvenhurst so that he could identify her if she ever tried to come near him. She finally sent him a letter with a gun and instructions to kill himself so that they could all be together in the end. I believe this was written about in a Rolling Stone interview with Michael shortly after Thriller came out.
The "Billie Jean" that's pictured in the earlier post is a lunatic who had been stalking him for years--tried to gain access to Neverland, sued him a bunch of times, claimed she was his wife, finally claimed that she was Blanket's mother and that Michael owed her child support. :smilerolleyes: She was either institutionalized or jailed several times, but kept getting released. She calls herself "Billie Jean Jackson." Even after Michael passed she was showing up at the estate hearings claiming to be Blanket's mom.