Star do go through cycles like that - when one fuel depletes and if the star is massing enough to fuse the former waste product. The transitions, such as from fusing hydrogen to fusing helium called the helium flash, are explosive and called novae. The Sun is not sufficiently massive to fuse helium. So it will fuse hydrogen in a shell around the core which moves outward to find fresh hydrogen and grows thinner. The larger the shell, the more heat it produces, causing the sun to gradually expand into a red giant. Comes a point when the shell is so large that the pressure above it is no longer able to sustain fusion. The end of fusion is quite sudden and the infalling of the star's outer layers immediate and catastrophic. There is a huge burst of fusion that throws off 10% of the star into interstellar space. That is a nova. In a star larger than the sun, this flash ignites fusion of helium into carbon in the star's core with a shell of renewed hydrogen into helium fusion around it and the star expands even larger than before since helium fusion is much hotter. Helium fusion does not last nearly as long as hydrogen so there are successive burnouts and reignitions of carbon, oxygen and silicon fusions in shells in stars 100 times as massive as the sun producing ultimately an iron core. Iron (and larger nuclei) fusion consume rather than produce energy. So when an iron star collapses, the infalling is not stopped but accelerated by new fusion. Heavier nuclei are produced in the last fraction of a second of the collapse and then are spewed into space in a recoil known as a supernova. All elements heavier than iron are the result of supernovae which fling a substanial part of their mass into interstellar space before the remnant settles down as a neutron star or black hole.
