How does the death of Hippolytus bring a change in the characters of Theseus and Phaedra?
Near the end of Euripides' Hippolytus, the title character is in the throes of death. He has been involved in a chariot accident that resulted in him being hurled out of the chariot car, tangled in the reins, and being dragged by his own horses.
Thus, at the end of the play, the dying Hippolytus is brought in for a final encounter with his father, Theseus, whose curse of Hippolytus prompted the chariot accident.
Before Theseus encounters his dying son, the goddess Artemis appears and tells Theseus about his wife Phaedra's false accusation of Hippolytus. Phaedra had hanged herself when Hippolytus rejected her sexual advances toward him, but, before she died, she wrote a letter falsely accusing Hippolytus of sexually assaulting her.
When Theseus learns the truth about what happened, he laments having actions toward his son. Thus, Theseus moves from being a man certain of the rightness of his actions to being a man who needs forgiveness from his son.
As for Phaedra, it is difficult to see how her character changes, since she has been dead for some time. I suppose, though, one might argue that in Theseus' eyes Phaedra moves from someone who had her husband's trust to someone who could not be trusted.