Could it be part of a broken egg, i.e. the membrane of the egg?
I would catch her, contain her- see if there are signs of yolk or other egg type debris around her vent.
Look up "digestive tract of a chicken" - there are pictures out there that show the real parts laid out intact from a chicken, that will help you decide if what you're looking at is intestines.
If the vent itself isn't prolapsed, I would be inclined to say that there's little chance it's her intestine.
Personally, I would utilize some lubrication and see if you can follow the protruding object inside the chicken to ensure you extract the whole thing. If it is part of a collapsed egg, it's important to get everything out. Sometimes a weak or shell-less egg breaks inside and the membrane collapses internally and then get wadded up by the hen as her muscles contract to lay the egg. When they lay one of those we often hear it described as "rubbery".