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Tear Jerker: Sayonara, Zetsubou-Sensei
Even the normally over-the-top ridiculous Sayonara, Zetsubou-Sensei has one of these in Episode 11 of the second TV series, when the girls sadly explain what has driven them to murderous insanity. "But... he never chose any of us."
The ending of Episode 11 is bad enough, as it moves completely away from the usual wacky and over-the-top tone. That's his entire class waiting for him outside the operating room. And if that isn't tearjerker-y enough for you, here's this AMV/parody ending.
I think I'm creepy. I just can't stand any part of myself. If I went to a picnic and saw my ugly face reflected in the lake, I'd just jump into it. If I went shopping and saw my ugly figure reflected in the show window, I'd bang my head against the glass and cut my throat with a fragment. My TV is always on. That's because if I turned it off, I'd see my ugly reflection. On sunny days, I have no desire to leave the house. Even my shadow is ugly. I'm an ugly manga child who'll never see the day when I become a swan. I changed the lightbulb over my sink to the lowest wattage.
The second-to-last chapter of the manga reveals that Kafuka is Dead All Along. Even worse, the last chapter reveals that her friends will eventually forget about her.