Thus, each annual layer starts 18O rich, becomes 18O poor, and ends up 18O rich.
This depletion is a temperature dependent process so in winter the precipitation is more enriched in H2(16O) than is the case in the summer.
The dating process is always designed to try to extract the carbon from a sample which is most representative of the original organism.
In general it is always better to date a properly identified single entity (such as a cereal grain or an identified bone) rather than a mixture of unidentified organic remains.
Obviously there will usually be a loss of stable carbon too but the proportion of radiocarbon to stable carbon will reduce according to the exponential decay law: R = A exp(-T/8033) where R is C ratio of the living organism and T is the amount of time that has passed since the death of the organism.