I'm very glad you asked. When our sun dies, the only people who will care are time travelers who attempt to return to earth. The people who have lived beneath the surface of our moon for thousands of years will will crack our moon's outer shell** and depart for their home planet in an unknown solar system near the mid-outer edge of the Milky Way galaxy. They will take with them two, and only two, dogs of the earth breed Beagle.***
**Archimedes, a former prominent moon inhabitant, is quoted: “Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.” This was based on his ancestors' use of such a lever-fulcrum pair to place our moon where we see it today.
***Also believed, but not definitively proven, to accompany these travelers are every know digital format of the Pink Floyd album 'The Dark Side of the Moon', Steely Dan's 'Aja' album and Return to Forever's 'Romantic Warrior' album -- and the technology for playback.