Not op, but I believe they're taking about "Jurassic Bark" season four episode seven. I won't spoil anything, but just know it's based on a true story, and that makes it so much more sad.
That one is sad, but the other one that I can't watch anymore is "The Luck of the Fryrish" with Fry's nephew. I cry like a bastard during the last scene.. no idea why.