If you remove just a small piece of gold, the necklace will still be there, albeit deformed.

Now, pardon me if I ask you the question since you seem to just want to go linear in your Q/As (I have these sets of questions that I expect these sets of answers to; any divergence from that would not be tolerated, seem to be your mantra). When you say you take away gold FROM the necklace, how? How are you taking gold away from the necklace? If you can answer this, I can give you the answer.

Now I know you will try to avoid answering that question. I will give you one way of doing so. Through electroplating, you can first cover this necklace with, say copper or similar metal. Then through electrolysis, you can extract all the gold from this necklace and deposit that in an anode. There you go, you now still have a necklace but no gold in it.