Please don't list this on a work's page as a trope. Examples can go on the work's YMMV tab.
Tear Jerker: Grim Fandango
"You were the best boss I ever had."
Salvador had a number nine ticket all along. Manny's reaction says it all.
Lola's death/sprouting. Never mind she was a minor character who previously appeared in a single scene with something like five lines of dialogue. Never mind Olivia flat-out told Manny that she was doomed due to her crush on Maximino. The worst part is when Lola admits she developed feelings for Manny at some point, but figured out it was hopless due to his obsession with Meche.
Lola: Tell me, Manny. Would I have had a chance?
(Manny looks away.)
Lola: Never mind.
And it gets even worse when Manny discovers a clue she left for him at Toto Santos's scrimshaw parlor. Upon hearing her name, the normally antisocial Toto suddenly lights up and confirms that she visited him earlier. "Sweet girl. Like a daughter to me. Tell her Papa Toto says hello." Manny just goes "Oh, right", and the game never makes it clear whether or not Toto eventually found out the truth...
Nick: Was...was that for the photo girl?
Manny: No, that was just for being you. I don't have time to get you for Lola, but I'm sure somebody will.
Not the best example maybe but Salvador's Heroic Sacrifice for some could be considered this.
In-universe, the story of beloved Sanspoof's death is so tragic that not even Manny, who normally detests cats, can resist getting choked up while he reads it.