White Timeline and Summary

After Black saves White from suicide, White arrives at Black's apartment (just before the play begins).
Although White keeps trying to leave, he lets Black talk to him and argue with him. White's willing to ask questions and gets Black to tell him a jailhouse story.
He accepts coffee from Black, and also joins him in eating dinner—which he really enjoys.
White starts defending his worldview more aggressively, and when Black runs out of arguments, White triumphantly praises death and the logic of suicide.
Finally, with no more options, Black releases White from the apartment. White walks out, apparently gearing up for another suicide attempt.