Norman Mailer wrote a book titled "Oswald's Tale". He came to the conclusion that Oswald probably did shoot Kennedy for his own reasons but he goes into detail about possible conspiracies which could already have been in existence at the time.
Mailer felt that the Mafia may have put out a contract on JFK and feared that Oswald might have carried out that hit. But instead of Oswald getting away or being killed, here he was on National TV alive and claiming to be "just a patsy".
Mailer's theory is that the Mafia, fearing Oswald would point the finger of blame at them, had him silenced by someone close at hand and able to get into the Dallas Police station: Jack Ruby.