@Wyorp Rock and I agree it's likely prolapse. This is a medical emergency and a reproductive crisis, about as serious as can happen in Chicken World. So, go catch her. I know how difficult it is, but get it done somehow. When I have such an uncooperative chicken, and yes, I do have a couple who hate me, I herd them into an enclosure of small enough dimensions that I can get the chicken in a corner and grab a leg. Once I make contact, I try to say calming words and slowly bring the chicken into my hands.
You should have a crate prepared to house her for the next day or two while you treat her. Line the crate with a couple of old absorbent towels. Have a basin of warm water ready to bathe her and soak off the mess on her vent and butt. Pat her dry and then give her a calcium tablet, calcium citrate is best, works fastest, but Tums will do. Stick it whole in her beak. She'll swallow.
Then place her in the crate with plenty of water to drink and some of her food. Leave her in a quiet place to rest, monitoring her frequently, but you don't need to handle her. Update us from time to time as to what she poops out, her behavior, what she eats, how much she's drinking, etc.
Hopefully, she's passed most of the material in her oviduct, but it's important to know if any loose yolk is expelled as she will then require an antibiotic. Once all material has been expelled from the oviduct, the prolapse should retract and not fall out again. At that point, she should feel noticeably better.