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Tearjerker: Invader Zim
The Sad, Sad Tale of Chickenfoot, where Chickenfoot talks about his past life with Dib where he was a normal man named Chewie Rodriguez until an accident occurred when the microwave was splashed with water while Chewie was wearing the suit and cooking chicken in a microwave, generating an explosion that "created an unholy fusion of man and chicken", causing him go insane and live all alone in an apartment with assorted Chicky Licky toys that he calls his "friends".
Bad, Bad, Rubber Piggy doubles as both horror and Tear Jerker worthy because of what Zim does to poor Dib by crippling him horribly by tossing rubber pigs into Dib's past through a time machine, replacing seemingly random objects in ways that cause Dib to have horrible accidents, progressively crippling Dib to the point that he almost dies.
"WHYYYYYYY?!? MY PIGGIE!!! I LOVEDED YOU, PIGGIE!! I LOVEDED YOOOU!!!!"
Bloatey's Pizza Hog, Gaz yells at Dib for going off to fight Zim because she "just wants to go out to eat with dad." Considering the situation, this certainly counts.
Bloaty. The poor man is completely miserable, and its possible we see him pass away at the end.
Although his situation is no less tearjerky, Rikki Simons confirms that Bloaty is alive.
How could one forget the MASSIVE tearjerker in which we see an adorable experiment in an isolated room of a spaceship, who hopes someone will rescue him... only to have ZIM nonchalantly leave? The poor creature is left to cry softly...
The ending of Dib's Wonderful Life of Doom. Poor Dib. Just when things were starting to look better...
"OH, GIR! GIIIIR! THEY'VE TURNED YOU INTO GROUND BEEF! HOW? WHY?????"
Dib and Gaz's.......situation. Their dad is so busy, they only go out to eat together ONCE A YEAR. Which seems sort of funny... until you think about it......
Dib finding out Dwicky's been lying to him in "Vindicated!" When you see how he joyfully and rather innocently reacts to someone extending a measure of kindness and tolerance towards him, it starts to kind of hit you just how ridiculously YOUNG the poor kid is, and when his "ally" is taken from him it becomes almost impossible not to see just how thankless and lonely a life he lives in trying to save his own people from extinction.
Dib: You don't believe me! You... (builds towards rage, then regresses to pleading, and winds up just staring at the ground in defeat) I thought you were different. Dwicky: Look, I know you think I lied, and I—I did, but I was only trying to help. Dib(bitter): Isn't this just great?! While you waste my time, Earth gets one step closer to being taken over! That's my problem right there! My problem is that the human race seems to want to be destroyed!
The hints to Miss Bitters' past, if you think there's any truth to them. Think about it: the creepy Humanoid Abomination that terrifies her students on a daily basis was at some point a normal person with hopes and dreams who got mutated into her current state by a freak accident. Miss Bitters may be a monster, but if these stories are true, can you really blame her?
Miss Bitters: I had a valentine once.
The ending of "Gaz: Taster of Pork". Ok, Dib might have deserved some punishment for using Gaz as a test rat for his spell drive (even though he did not do it out of ill will), but not only tricking Dib into believing she was still in danger when she obviously was not but also forcing him to clean up Shadow-Hog dookie with his head while he's crying for forgiveness? Not to mention all the horrific (and very graphic) death threats and beatings that Dib took from her while he was trying to help her? No wonder Gaz has a bit of a Base Breaker status.
Well, there was also the horrible experiments that Membrane most likely did to her during her quarantine. It makes it worse knowing that her dad is the only person she has/shows any value for... and since it kind of was Dib's fault and she already has A LOT of disdain for him...