When a hen is not eating or drinking and it's making her weaker by the day, tube feeding may be necessary to get nourishment and hydration into her. I usually tub feed once or twice and that usually gets the chicken eating and drinking again. Tube feeding is strictly a short-gap intervention...
It does appear to be lash material. This stuff is pus and indicates reproductive infection. It would answer why she isn't laying eggs. You can try to treat the infection with an antibiotic such as amoxicillin, but by the time you see pus sloughing off, the infection is usually pretty far along.