Partially swollen vent, and she's trying to pull something out

I've heard of hens getting egg-bound, but I am not really sure how to recognize it. One of my SLWs has been sitting in the nest box and not really producing an egg, but since we are not out there all that often, and since it is difficult to tell the 4 SLWs apart, I don't really know if this is a recurring problem, or if I am seeing a different one in the box actually laying.

Just now I noticed one of them outside picking at her vent, and something poo-like seemed to be coming out. Is this normal behavior? Or something I should look into more closely? These 4 are hard to capture and look at, so I am not sure what I would do to get a closer look...