Why didn't the Thebans avenge the king's death in Oedipus Rex?
Within the first few pages of the play, we are presented with two possible reasons why the Thebans did not make a concerted effort to locate and punish the killer of their slain king, Laius. First, we find out the circumstances surrounding the king's death. When Oedipus asks Creon who returned from the king's party at the time of his murder, Creon says: "All slain.... One panic-stricken fugitive / Told naught that he saw—knew naught—save one thing only."
The "one thing" is that the king and the majority of his party were killed by a large company of robbers. From this conversation, we can deduce there was little information to help track down the king's murderer. This is part of what deterred the Thebans from avenging the death of their king.
Secondly, the city itself was rife with problems. At the time of the murder, the Sphinx advised the people to not pursue the king's murderer but focus on other hardships. Thebans heed the word of the Sphinx as though it were law. As Creon explains: "It was the Sphinx—whose riddling song constrained us / To leave the unknown unknown, and face the present."
(Now, however, the Sphinx advises Thebes to address the former king's murder, that "fell pollution, fed on Theban soil.")
When Oedipus begins his quest for the truth, seeking out King Laius' killer in order to eliminate the plague placed on the city, he asks many questions in order to determine the true killer of King Laius. While Oedipus questions Creon about the details surrounding the murder of King Laius, we discover that the citizens of Thebes did not continue searching for the killer due to the terrible circumstances that the city faced. Oedipus is informed that due to the curse placed on the city by the Sphinx, the citizens were not able to continue searching for the killer due to the fact that they were so overwhelmed by the state of the city. This means that the citizens were never able to find the murderer prior to Oedipus' discovery that he himself is the killer, which explains why they did not avenge Laius' death.