That seems to be a forgotten story element, much like the poor little Borg baby in Voyager.On another note, what happens to the phaser that the bum destroys himself with? I don't think it would be destroyed along with him. Perhaps it was found by the CIA...
However, someone wrote a wonderful essay in Best of Trek called "The Disappearing Bum" where he speculated that the bum's death is why there is no Star Trek the TV show when Kirk and Janeway visit the late 20th century (in 1984 and 1996, respectively). The author suggests that the bum had a family to support, and when he didn't come home, they thought he had abandoned them. The oldest son then had to take on the responsibility of feeding his mother and siblings... and later in life, he continued the life of crime started during the Depression years. He ended up in Los Angeles, and happened to meet up with a certain police officer... and killed him. The police officer was Gene Roddenberry (as GR was once a police officer), and since he was killed before he ever thought of Star Trek, that's why Kirk and Janeway weren't beset by hordes of fans!
CANON VIOLATION!