sounds like a chicke that didnt develop in the shell properly....this can happen if bator temps are not properly controlled or in cases where a chick is "helped" to break free. it's best to let nature take it's coarse and double check your bator temp make sure you have an accurate thermometer and if it's a styrofaom bator increase the temp to around 100.5-101F instead of 99.5F
Sorry you had to experience that. It happens. Breaks my heart every time, but it does happen. I had an awesome rooster that I knew we would have to put down soon as he had an incurable, seemingly painful leg condition that just wasn't improving. Before we put him down I managed to get ONE egg from a hen that was the same breed and color as he was - dark brahma over dark brahma. The chick was beautiful, but also way too large, had a hard time hatching, was partially paralyzed. I wanted that chick soooo bad, but it was not to be.
I'm a wimp, can't cull my own birds. My husband takes them to the far end of the farm and does it for me. I cried when he euthanized that chick. Cried even harder when he put the roo down a few days later.
If you are going to raise poultry, sooner or later it's something each of us to face. Worst part of keeping them, but necessary. You did the chick a favor. (((HUGS)))