DHH's father, HYH, is the character that dies in the course of the play. DHH, of course, is David Henry Hwang, and HYH is Henry Y. Hwang. It's not a plot point that we see occur, but it is mentioned through narration - the reading of his obituary. It creates a poignant moment for the audience, who has been tangled in HYH's enthusiastic story of the American Dream, even after being accused of treason. HYH was a good foil for DHH throughout the play, bringing the arguments of the dominant group into play, along with injecting some humor into the situation with the conversations between DHH and HYH.