Yes. Since it is smaller than most other stars, it uses less energy.
A star is a nuclear reactor, except instead of splitting atoms like in an atomic bomb, it fuses atoms together. The sun (which is just an ordinary, unspectacular and pretty small star) fuses so much hydrogen per second into Helium that the reaction creates the helium with a bit of energy left over, and that bit of energy left over becomes the heat and light that we get from the sun.
When all the hydrogen has been converted (you can't say burned; this isn't like a log fire) into helium, the helium tries to keep the fusion reaction going by fusing its atoms together into another, even heavier, gas. Once all the helium has converted, each of these heavier gases convert until there is nothing left to convert to, and the reaction stops. For as long as there was a fusion reactor going, this was enough to resist the forces of the star's gravity, but now, gravity takes over and starts to collapse what is left of the star. If the star is many times more massive than our sun, this rapid collapse could cause a supernova as the star explodes. If it is super-massive, then it could collapse completely and become past the white dwarf stage to become a black hole, which is where gravity has taken a truly huge star and collapsed it to something the size of a ping-pong ball that would weigh hundreds of billions of tons and has a gravity so hugely powerful that not even light can escape.
Our sun isn't big enough to explode in a supernova, and far too small to become a black hole, so it will collapse just far enough to become a white dwarf; a burned-out remnant of a star.