I had something similar happen to a chicken last summer. The chickens were free ranging and we went to a river beach in town. We came home and one of the 12 had been taken, and my girl Wynonna looked very disheveled. Half her tail feathers had been ripped out(I found them in a little pile not far away), and her actual tail nub was torn in half. Through the muscle.
I rinsed her well with lukewarm water several times, and then a few times with hydrogen peroxide, to get the deep dirt out. I did another rinse, and after she was in her roost for the night, I applied Neosporin. I Rinsed it out the next morning, and let her go about her day as the bleeding stopped. She dust bathed during the day, so just before bed on the second night I flushed with hydrogen peroxide. The next morning, there was a thin scab covering the area so I left it alone.
I monitored the scab edges for about a week, making sure the edges weren’t looking red or inflamed, and gently pressing with my finger to make sure puss or fluid wasn’t collecting.
Her tail never healed back together(it’s two mini nubs now

) but she is healthy, fully feathered and fabulous. Definitely the boss lady of our flock. The most adventurous and outgoing, always the first one out of the run and up in my business each morning.
I personally wouldn’t cull yet. Id treat the wound as I described above, monitor behavior, and make the decision based on your chickens temperament and appearance of health.