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Hello and thank you for using this site to help you. You are right to be concerned and if this just happened you can call your vet as they may be able to retrieve the bone piece using a scope.
If you wait it out depending on how big a piece it was then the dog may or may not pass it and it can cause an obstruction which requires surgery.
You can try giving some pure canned pumpkin to help move the bone through but if you see signs of sudden lack of appetite, vomiting, diarrhea or change in stool, and lethargy you are looking at an obstruction.
If there was meat on the bone then you also have to worry about pancreatitis which would show many of the same symptoms as an obstruction.
another thing to worry about is if the bone splinters and pierces the intestinal tract.
Here is more on obstruction. http://www.petplace.com/article/dogs/diseases-conditions-of-dogs/stomach-intestine-liver-or-pancreas/gastric-stomach-foreign-body-in-dogs