All stars, whether variable or single and stable like Regulus, the Sun, and Proxima Centauri, eventually exhaust their hydrogen fuel. At this point, gravity begins to "win" as the star's energy output drops. The gas pressure goes down and the star contracts under its own gravity. However, contraction raises the core temperature even more, and stars like Alnilam, Regulus, and the Sun will all be able to eventually begin new fusion reactions involving helium, rather than hydrogen, as the fuel. The ashes of the previous reactions are now used as the fuel for the new ones. This process of finding progressively heavier elements to burn causes the stars' radii to increase dramatically, at which point they are called giant or supergiant stars. Alnilam is one of these; it is a blazing supergiant, fusing elements heavier than hydrogen in its core, and shining with the light of 30,000 Suns. If we were suddenly to replace the Sun with Alnilam, the earth would become a broiling wasteland in very little time.
Eventually the star fuses the last element it can use as a fuel source (for massive stars, this element is iron), and the result, as usual, depends on the mass: Alnilam will blow itself to bits in a supernova, and the dead remnant will be a neutron star or a black hole. The Sun will eject its outer layers more gently, in an expanding cloud of gas called a planetary nebula, leaving behind its carbon-and-oxygen core as a small, glowing object called a white dwarf. Proxima Centauri will do none of this. As its hydrogen runs low, an unimaginably long time in the future, it will slowly cool off as a slowly dying red dwarf.
Science EncyclopediaScience & Philosophy: Spectroscopy to Stoma (pl. stomata)Star - Energy Generation, Stellar Models, Mass: The Fundamental Stellar Property, Four Stars, Variable Stars - The nature of the stars