I'm pretty new so take everything I say with that in mind and ignore me if an expert chimes in.
That said, I would keep an eye on her. If you can see what her poops look like that would help you determine if she is ill. Mine will droop their tails down on occasion if they're afraid and they do it while on the roost bars but walking around like that all the time usually is a sign that someone isn't feeling well. I wouldn't just start medicating willy nilly until you know for sure she's sick and what she probably has (otherwise you wouldn't know how to medicate.)
How does she look otherwise? Is she eating and drinking? Are her legs smooth and shiny? Any discharge from the nostrils, beak, eyes, etc? Again, how do the poops look? What is her behavior like? Normal other than the tail?
Could be nothing but like I said, keep and eye on her and watch for symptoms. The Emergencies/illness (etc) thread is a great place to post if you're concerned and find other signs of illness. HTH.
Thank you for your help!! I watched her all day today and she is eating and drinking and her poop looks normal. No discharge from nose. Eyes look clear so she does not seem to be sick. I think that bottom of the pecking order makes sense because when I feed them a treat, I can throw something right to her feet and she will not eat it and lets the others eat it instead and I have seen the other hens peck at her. It can be a cruel world for a chicken if she is last in line on the pecking order. Thank you again for your posts.
My (limited) experience is that the tail down is a sign they are not feeling well. In both cases I confined the bird in a dog crate in a quiet place and put Corid in the water for Cocci. By the end of the day they were feeling back to normal and I returned them into the flock.