Carbon is an element. Most organisms to a lot of chemical rearrangement of the element, but the element is not created or destroyed in biological processes. Any carbon kept during life is released at death.
We have found shells, made of Calcium carbonate, still relatively intact more than 3000 years after the death of the animal. Some shells had last for 500000 years (See Nature 2014-dec-03)
Under the sea there are entire ecosystems based in dead shells.