Stable isotopes are not radioactive.

They do not decay.

They do not participate in the freshwater reservoir problem in the same way.

What they record is the ratio of different stable forms of carbon (carbon-12 and carbon-13) and different stable forms of nitrogen (nitrogen-14 and nitrogen-15) in the organic material being analyzed.

These ratios vary in systematic ways across different food sources and environments, and they are incorporated into bone collagen during the years when that bone is being formed and remodeled.

They provide, in effect, a chemical record of what an individual was eating over a span of years.