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Tearjerker: Circle of Magic
The scene in Shatterglass where Tris comforts Glaki after her foster-mother is killed by the same person who killed her mother.
That and Tris, Keth, and Chime's reaction to discovering the body law enforcement found was Yali's.
Briar's Book: Briar's street rat friend dying, the awful time he and Rosethorn spend in quarantine, Rosethorn's catching the plague and the subsequent events, just to name a few.
There's a line in that book that's easily missed, but hits hard if you've become familiar with Lark and Rosethorn and their relationship.
Only yesterday she had seen Lark work her most powerful charms to keep Rosethorn safe. Not two hours [ago], when Sandry had brought fresh linens to the sickroom, she had discovered Lark weeping, her charms in her lap. All of them had fallen to pieces, unable to work in the face of Rosethorn's disease.
All the fires in Cold Fire. A blind girl nearly dies because she couldn't escape, a maid and Daja work to save children and babies only for the maid to suffocate and several of the children die, a homeless woman sleeping in the basement of a shop burns to death, the furnace of a bath-house explodes, an entire hospital is set on fire... Pierce doesn't stint on showing the aftermath and the grisly details, either.
Battle Magic has a long list of these. Special mention to Briar's reaction to the news that Evvy is dead.
They killed Evvy's cats.
Luvo's sincere attachment to Evvy combines with his Innocently Insensitive nature to both warm and break your heart. He sends a snow leopard to confirm that Evvy's cats are truly dead, and breaks the news as gently as he knows how to. Later, he picks up on Evvy's distress and storms in to help her, only to find her in the grip of PTSD and desperate to leave Gyongxe — Luvo's home. Bewildered and anxious about separating from his new friend, he tells her "I can find find you small, furry creatures. There are many of them here." It's obvious that he doesn't understand why Evvy is so torn up about the loss — he's just desperate to make her hurt go away so that they can stay together. The whole scene makes you hurt for Luvo and Evvy...and strikes close to home for anyone who's been told by well meaning friends "just get a new pet.