Rescued chicken with distended vent.
Without seeing what is going on, "distended" can mean one thing to you and another to someone else. Pictures will definately help.
But with your description just off the top of my head two things come to mind prolapse or vent gleet.
There are a lot of articles/threads and treatment about each one BYC and here is an article on each one (with photos) to get you started.
Hope this helps.
Glad to hear this! Maybe she was a bit stressed from being moved and really needed to lay an egg and was unsure what to do? Never know.
I'm sure you will take good care of her.
Wishing you continued health.