To elaborate, the family chase after their father when it seems like he's chasing Alan with a tanto knife to kill him (because a televised suicide failed when the government inhaled laughing gas instead of poison which could lead to their shop being closed down) only to find out that Mishima was actually planning to kill himself. This leads to a chain of suicidal threats from other family members. Alan begs for them to stop, but then he stumbles and falls off the tower's window though he managed to hold on with one arm. The family (and Marilyn's husband), work together to save him by lowering Vincent's bandage turban to pull him up. The family suddenly began to talk about their future and share a laugh. Alan, upon noticing their new outlook on life and the smiles on their faces, decides to let go as it is implied that he has done his life's work.
The hope spot in the second to the last paragraph makes the conclusion all the more tragic.
Madame Tuvache watches [Alan] approaching as if she has suddenly seen her mother arrive in the school playground.note In one chapter, Lucrèce reflects back on her childhood when her mother, who was often late or never came at all, would pick her up from school
The way it ended in itself. It was so abrupt that it doesn't even give the chance for the family (and the reader) to grieve his death.
Mishima and Lucrèce's song about how they must stay alive in order to help people commit successful suicides to ensure happiness in their own suicides. By the end of the number, both were in tears.
Before that, when Mishima was out to kill his son, Lucrèce can do nothing but beg for him to stop. She even threatened suicide if he killed their child.
