I am a suburban chicken owner but I've only killed two chickens young.
1) One Rhode Island Red stubbornly refused to get off of her eggs, like randomly. This was around 10 years ago and we had no roosters at the time (even though we lived in a municipality that allows them, which my current town thankfully does not because roosters are the devil incarnate) so her eggs weren't fertile, so I was like wtf. She did this for day after day, getting weaker and weaker until I got pissed and pulled her off the eggs and basically showed her how to be a damn chicken again. She was good for a few days, showed no health problems, then after a week or two she started doing it again. She wasn't eating and she wasn't drinking, and she got weaker again. None of the research I did proved particularly fruitful. I pet her and gave her some of her favorite foods, and then put her down humanely like a wannabe farmer should. She did not go to waste.
2) This one was hard, because it happened last year so my daughter was old enough to know what was going on. We had a beautiful white hen named Snow, and she broke both her legs falling off the stairs to her coop. We took her to the vet (because I believe that once you name an animal, it ceases being pure livestock and becomes at least partly a pet) and he said she probably had an extremely rare condition that made her bones very fragile. I f***ing raised this one from a newborn, it was tough letting her go because she almost died in her first few weeks but I at least partially willed that mother f***er back into life through sheer effort and desperation. However, a chicken that can't chicken isn't a chicken anymore. We let my daughter spend the day with her, and then we euthanized the bird. Even today, every once in a while, she'll say "What happened to Snow?" and explaining loss to a 3-year old is not fun even for something like a pet chicken.