They can pass parts of egg, but infection may be the cause. Salpingitis, egg yolk peritonitis can be possible. I will tag @casportpony for any expertise.
Bright yellow droppings can be a sign of E.coli infection. Can you get antibiotics from a vet, or have her seen? The best antibiotic for her is enrofloxacin (Baytril,) which is banned for chickens. Some vets still will prescribe it because it treats E.coli, Mycoplasma (MG,) and other...