A cat will continue to walk while in it's sitting animation. This was reported to me via a member of the Lifeboat Network moderation team. While this didn't take place on the server, it is best to report even the smallest of issues a player experiences. I don't know how to reproduce this, but it seems like you need to tame a cat, and then tell your cat to sit. This should re-create the bug.
Because the video is too big, I have made it into a YouTube video.