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Tear Jerker: Excel Saga
Excel Saga actually advertises episode 24 as a Tear Jerker. And as promised, not a single joke in the entire episode (except for one brief one where Kabapu is revealed to only be pretending to bleed). Still, for fans of this Gag Series it's usually rather uncomfortable to see Excel get a really drawn out death scene while she's bleeding and monologuing. Not that she seems to know about such things though, given her "something is flowing out of my body" comment. The rest of the episode isn't much more cheerful, with most of the characters actually getting a bit of serious Character Development.
To specify, that was the following episode which was serious. But the real tearjerker occurs in the previous Wham Episode where, after an episode that was mostly a parody of Fist of the North Star, the last couple of minutes has Excel banging on the door of Il Palazzo's base until her fists are bloody and crying out for Il Palazzo to let her in, only for Il Palazzo (who, unbeknowst to Excel, is Brainwashed and Crazy) to shoot her through the chest and leave her to die in the desert. It was just so pathetic and sad.
There's also the episode 8 where Cosette is assigned to an assassination mission. Her mark is a lady that Cosette can't kill after realising she has a daughter; this triggers Cosette's memories of her own mother's death. All fades to black, Cosette sees her mother's spirit at the distance, waving goodbye. Cosette wants to follow her but Pedro shows up to pull her back, since she would die if she went further. Oh, Cosette's mother gets better by way of Izi-chan.
Oddly enough, this entire sob story was clearly meant to be a parody of a Tear Jerker.
The systematic elimination of of Wolf and the Dog Pack in episode 10. The subsequent betrayal by Inchiki and Menchi's kind previous owner, who ended up NOT being really kind at all. And Menchi's sad song during the credits. It always plays on the credits, but this time it was poignant.
And the continuation of "Menchi's Great Adventure" in episode 19 is no more cheerful. Menchi meets a rich but lonely girl who became possibly the first human to ever genuinely adore Menchi, she then accompanied the girl on a happy trip around the world. Later it is revealed that, some time ago, the girl had also met and became friends with Wolf from episode 10, she tells Menchi that she misses Wolf and wonders what he is up to. Even later, Menchi gets to witness the girl being shot dead by that same crooked old man who killed Wolf in episode 10. But this being Excel Saga, Mood Whiplash ensues, and the whole thing ends up feeling hilariously bizarre.