It is possible for a dog to eat a necklace and if she does not pass it through the stool then it may become an obstruction of the bowel. Symptoms of this are sudden lack of appetite, vomiting, diarrhea or change in stool, and lethargy. An obstruction would require surgery. I would suggest that you have her x rayed to see if the necklace is inside her and where inside her it is.
Here is more on obstruction. http://www.petplace.com/dogs/gastric-stomach-foreign-body-in-dogs/page1.aspx