My two have done that at times, and, it just makes them feel bad, since their digestive process' have been interrupted/slowed. If it was a Bully Stick, I rather doubt if there's any chance of damage, given that the ends aren't sharp. Given time (a day or two) the material will yield to their intestinal process, and they'll be back to normal.
I use a lot of Bully Sticks, so, this "problem" has a chance to happen frequently. When noticing the need for removal of a short piece, I ALWAYS get a couple pieces of Cheese. Distract them with it, and scoop the shorty up and away. At this point, they are quite used to the little Sticks disappearing. Probably think it's Magic.
