Why did the lone surviving slave of Laius's party plead with Jocasta to leave Thebes when he saw Oedipus on the throne in Oedipus Rex?
The messenger who brings news of the death of Polybus, Oedipus's father, tells him that Polybus was not his birth father. Instead, he says, many years ago a shepherd gave the baby Oedipus to him, and he took the baby to Polybus and Merope, the king and queen of Corinth, who raised him as their own. Oedipus demands that the shepherd be found and brought before them. When this shepherd, once a slave belonging to Laius, arrives, he confirms that he and the messenger used to tend their flocks together when they were young, and he admits to giving the man a baby many years ago. When the messenger tells the shepherd that that baby is Oedipus, the man now in front of him, the shepherd grows very upset, and he tries to resist answering any more of Oedipus's questions because he knows that Oedipus has, in fact, married his own mother, the queen, Jocasta. He eventually explains that he was given the baby, all those years ago, by Jocasta because a prophecy had foretold that the baby would, one day, murder his father, Laius. It is in this way that Oedipus learns that he has, in fact, fulfilled this part of the prophecy which the oracle at Delphi delivered to him.
Laius' sole surviving slave (now working as a farmer) begged to be allowed to leave when he realized who Oedipus was, specifically, Laius' murderer. Oedipus in his arrogance has sworn that he will rid the city of Thebes of its plague by finding the murderer of Laius, not realizing that he is the one who killed Laius, nor realizing that he is in fact Laius' son, destined at birth to kill his father and marry his mother Jocasta (which he did). Jocasta is trying to learn more about her late husband's death and so interrogates the slave for information, yet the slave fears Oedipus' anger if he should tell him the truth. Therefore, he sees leaving Thebes a safer option than telling him who the murderer is.