What happens to the chemical elements that make up the molecules of living things as they pass through a food web?

What happens to the chemical elements that make up the molecules of living things as they pass through a food web is that some of their energy is stored in newly-made structures.
When molecules circulate freely like that, they become energy at some point. Especially if they are eaten by organisms - then the energy they become is stored in those organisms and used for everyday functions such as moving, eating, and generally living.