The sun will enter this phase of its life as it ages and the hydrogen/helium reaction reduces. See the Wikipedia extract as follows. There are also articles on Red Giant and Asymptotic Giant Branch stars in Wikipedia

When a star exhausts the supply of hydrogen by nuclear fusion processes in its core, the core contracts and its temperature increases, causing the outer layers of the star to expand and cool. The star's luminosity increases greatly, and it becomes a red giant, following a track leading into the upper-right hand corner of the HR diagram. Eventually, once the temperature in the core has reached approximately 3x108K, helium burning begins. The onset of helium burning in the core halts the star's cooling and increase in luminosity, and the star instead moves back towards the left hand side of the HR diagram. This is the horizontal branch (for population II stars) or red clump (for population I stars). After the completion of helium burning in the core, the star again moves to the right and upwards on the diagram. Its path is almost aligned with its previous red giant track, hence the name asymptotic giant branch. Stars at this stage of stellar evolution are known as AGB stars