It sounds like your chicken might be suffering from a problem with her oviduct, that may have progressed to infection. They can lay parts of eggs and membrane at random times. What do you feed? Do you have crushed oyster shell available for extra calcium? If you have human calcium tablets with vitamin D, you could give her one daily in the back of her beak, for the next few days. If vet care is possible, they may prescribe an anti-inflammatory drug and strong antibiotic. Baytril is sometimes used, but amoxicillin for fish is fairly easy to obtain in some feed stores and online (Aqua-Mox or Fish Mox.) Water is very important if you can hold a small cup up to her beak. Electrolytes or sugar water might help.
