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Although it IS okay to end a side story as soon as a character is killed off; it is NOT appropriate (i.e. seen as good writing by readers) to end a story without resolution of the character's arc. ...
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#4: Attribution notice removed
Source: https://writers.stackexchange.com/a/45957 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#3: Attribution notice added
Source: https://writers.stackexchange.com/a/45957 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
Although it IS okay to end a side story as soon as a character is killed off; it is NOT appropriate (i.e. seen as good writing by readers) to end a story without resolution of the character's arc. The "surprise" ending of this POV you outlined will be seen as crappy writing, it will not evoke any of the emotions you seem to think it will. In this case, the way to handle this character's downward arc is prophetic depression and foreshadowing. The foreshadowing is to put in his story line somebody much like him, say Joe. Similar background, similar interests. Joe is also promising to return to his wife, Emily and his child, Alicia. They become friends. Then he watches Joe get killed, and it shakes him; that his _friend_ could not keep his promise. After his friend gets killed, his commanding officer asks for volunteers to gather Joe's effects; and among them our hero finds a letter. "Dear Emily, Dear Alicia. I am so sorry I won't be with you, ..." A death letter. Our hero is in war, death of men just like him is all around him. The "prophetic depression" is him realizing he isn't that special, they all promised to return. When he gets his final order, their mission sounds bad enough his fear breaks. He sits down and writes and his own death letter, stuffs it in his pack, and marches into battle. In other words, to complete his arc, you need to tell all about the consequences **after** his death, **before** his death! You do that through proxies or stand-ins for himself, so he actually experiences some semblance of the emotions he _would_ feel if he could feel, after his death, through empathy and sympathy with his fallen fellow soldiers, (those are "foreshadows") and turning the deep depression he _would_ have felt by failing his wife and child into a prophetic depression; before the battle he just _knows_ he is not going to make it.