The symbolic Oswald
Because DeLillo's version of Lee Harvey Oswald differs substantially from the normal depiction of him, he can be said to be symbolic. He symbolizes two things at least: he symbolizes the version of the story that people prefer, which is to believe that he is some conspiracy-oriented super genius, and he represents the version that DeLillo prefers, which is that he is a pretty regular guy with a normal life whose life took a wild turn.
The assassination
The novel can be understood as a depiction of all the associations one could make to John F. Kennedy's assassination. DeLillo explores the symbolism thoroughly, observing in liquid prose all the ways that the assassination changed public opinion. The assassination represents a change in the feeling of the nation, and it changed the world. As a symbol, it also represents the height of conspiracy.
The Cuba theory
This symbolic theory represents an angle that few conspiracy theorists consider, at least in the main stream. The idea is that perhaps the assassination was actually designed by the government, except that it was a stunt design to provoke war with Cuba. The idea is surprising, because the success of the attempt would have been a jarring change in the plan of the conspiracy. This theory represents the horror of plans gone wrong, and it represents the opposite of the normal conspiracy approach.
The motif of regular time
The novel explores the strangeness of regular time, which represents the strange interconnectedness of daily life. If the assassination warrants extremely focused, creative attention, this novel suggests that such an approach might be a wise approach to normal time and daily life. The motif is primarily illustrated in the normal daily life of Oswald and the host of minor characters.
The symbolic blame game
The novel quickly dissects various approaches to government. There is Oswald and the Communist party, and there is Kennedy and the free market, so quickly the whole nation rallies around Capitalism, hoping to blame the incident on Communism. DeLillo's writing makes this into a symbol for cognitive dissonance, because there is no reason to suspect that it wasn't designed to look a certain way by any government agency. DeLillo's book symbolizes the desire to have a specific enemy, which he criticizes.