Have you examined the soiled area up close to make sure it's not mites or other parasites?
If she has chronically runny poop, she may be sick with something. Does she eat okay? Does she stand around, listless with her tail down?
If it's negative on all the above, she may simply be a candidate for an occasional sponge bath to "tune up" her fuzz butt. It's easy to do. Prepare a small wash basin with warm water and children's bubble bath soaking liquid, (I use the formula for sensitive skin/no tears) and back her up to the basin. Splash warm water onto her rear until the crust loosens, then pull it off the feathers. You can use a soft wash cloth to gently clean around the vent.
No need to rinse. Towel dry or blow dry. I do dirty, feathered feet this same way. Backing a chicken up to the bath seems to work best, dipping one foot, then the other so they don't feel off balance.
All my flock get touch-up baths as needed. No need for filthy chickens. They're washable!
