What would happen to Earth if the Sun didn’t exist?
There can be no photosynthesis without sunlight. Crops would cease to grow. Depending on the season, we may or may not receive one more harvest! Our herbivores would soon starve as they chewed their way through the last remaining foliage. We'd soon be starving as well. If the sun abruptly departs, Earth will experience absolute darkness after 8 minutes - the time it takes for its light to reach us. If darkness were the sole influence, it would take a long time for most life on Earth to perish.
However, there would be a quick drop in temperature, making survival more challenging. Because the sun is the center of gravity in our solar system, its departure would cause temporary anarchy among the remaining components, and the system may establish a new center after a few collisions. Perhaps Jupiter, or a new massive planet created as a result of Jupiter colliding with other things orbiting the sun. If Earth is fortunate enough to dodge these collisions and does not just fly out into space, it may begin to revolve around the new center.