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Tear Jerker: Axe Cop
Ask Axe Cop #15. The composition of the last panel is one of the most poignant.
Ask Axe Cop #52. The sheer amount of effort Sockarang puts into making love possible for him is just inspiring.
The epilogue in issue 3 of Bad Guy Earth.
The destruction of the nameless alien race, which included Sam and Max's foster parents. (Episode 153)
In the animated series, after killing Bad Santa, Axe Cop mentions how the day his parents died was both the best and worst day of his life. "Actually, I wasn't happy or sad... I was medium. And medium is the happiest I'll ever be." He then walks away, shouldering his ax. Surprisingly deep for a character like Axe Cop.
Becomes even deeper with Ethan mentioning that it wasn't added by the show's crew; Malachai wrote that scene for for an unfinished Ask Axe Cop comic. It says a lot about how Malachai is maturing.