This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / .hack//AI Buster
In the .hack//AI Buster light novel, the climax: The little girl NPC, Lycoris, who has been following along with Hokuto and Albireo, calmly asks him if he is going to kill her. He replies that she is just a vagrant AI, which isn't supposed to exist in the game; it's not "killing", it's just deleting an error. Hokuto isn't aware that Albireo is an administrator and Debugger, and can't understand why he would do this. As his spear passes through her, the room is altered, and Lycoris shares a memory fragment with him. She reveals that there's an intelligence at work in the game that deemed her a failure, and was trying to get her deleted. Lycoris admits that she's tired of running, and that she only wanted to become whole again. As Albireo begins to change his mind, she gives him the one thing that will give him the ability to delete her, and before he can stop it she's gone. He is so distraught by these events that he ends up quitting the company, sowing the seeds for Kamui's own path down the Knight Templar road.
A followup scene in the Legend of Twilight manga has Zefie, Aura's AI daughter created to enable the experience of motherhood, traveling through the Net Slums, which are an area of leftover data and partially deleted remnants. A girl appears before them: Zefie and the girl stand face to face for a moment. The girl asks if Zefie is seeking the end. She warns that the ending may not be as Zefie expects it, and asks again if she intends to follow through. Zefie answers that Yes, she will accept their ending no matter what comes of it. The girl smiles and replies, "I hope your ending will be kind to you... Good night." and disappears... Leaving behind a single Lycoris flower that falls to the ground. When Zefie's companions ask her what that was about, she simply replies, "She was a long forgotten piece... of some very old data." while picking up the flower. At the very last panel of the book, Aura and Zefie are shown waving goodbye, still holding the Lycoris. Who knew AIs could be so sweet?
Read AI Buster and then just try to read the later chapters of Legend of the Twilight Bracelet without needing a hug.