Listless chicken with feather loss around backside

Is the white stuff just on the feathers, or is it on the skin, possibly accompanied by white sores? And is there a foul smell near her vent? If so, then your hen probably has Vent Gleet, which is a fungal infection.

If its just white stuff (most likely urates from the droppings), then there isn't much to worry about. Some hens just don't keep themselves clean. Often times, at least with my birds (especially during wet/cold times), a bird will be dirty for several months, and then suddenly not have any problems anymore. If you want to clean her up, give her a nice warm bath.

However, the fact that your hen is droopy is a bit more alarming. How old is she? If over a year of age, she could be molting, which would explain the feather loss and pale comb/wattles. If not, worms or Coccidiosis are my two main suspects. Both cause chickens to be weak, with pale combs and wattles. If you see no improvement after worming, I'd treat for Coccidiosis.

Probiotics and/or yogurt might certainly help, if it is just a slight digestive issue, so I'd try those as well.