Kenji Fujimoto is the pen name of a man who alleges to have been Kim Jong Il's private cook from 1982 to 1996. Following his escape and defection to Japan, he wrote a series of books detailing both his life inside North Korea and that of the ruling family.
Among other things, Kenji details that Kim Jong-Il was severely affected by his father's death and entered a deep depression. He goes on to say that Kim Jong-Il was contemplating suicide and was at one point found with a gun.
So, what if a few months after his father's death Kim Jong-Il actually kills himself?