Carbon atoms come in a couple of “flavors” called “isotopes”. The vast majority of carbon atoms are of the variety known as Carbon-12 (they have 6 protons and 6 neutrons in their nucleus). These Carbon atoms are stable and last, for all intents and purposes, forever. A certain (and rather well established) percentage of Carbon atoms come in the flavor of Carbon-14 (they have 6 protons and 8 neutrons in their nucleus). These atoms of Carbon are not stable, and will eventually undergo a process called beta decay to “balance” the number of Protons and Neutrons in their nucleus. When it does, it changes into a Nitrogen 14 atom. The other “normal” Carbon atoms are unaffected. There will always be Carbon present in an organic sample, no matter how old. It is only the UNSTABLE Carbon atoms that decay. Now, after several million years, you won’t find much of any Carbon-14, as it has a half life of about 5700 years or so.