Hi Eliana,
That's an interesting question.
Most life on Earth depends on energy from the Sun in one way or another. The Sun warms the Earth and drives the convection currents in our planet's atmosphere that create weather. Plants need sunlight for the photosynthesis reactions that convert carbon dioxide and water into the materials they need to grow. Without sunlight, there would be no plants for animals to use as food. Too much exposure to the ultraviolet radiation in sunlight can give people a bad sunburn, but humans actually need some exposure to sunlight so their bodies can produce vitamin D. Without the Sun, there would be no life as we know it on planet Earth. It would be very difficult, maybe even impossible for the people, animals, and plants we are familiar with to adapt to living without energy from the Sun.
From what I know about stellar evolution, it is likely that life on Earth will have disappeared long before our Sun burns out completely. If you look through the other posts about the Sun's death and stellar evolution posted on the Solar Week message board, you will learn that someday the Sun might expand into a red giant and engulf the Earth. Life as we know it could no longer exist on Earth at this stage in the Sun's evolution. Unfortunately, we can't just replace our Sun with a brand new one when it dies, the way we replace a light bulb. Our Sun and solar system took millions of years to develop out of the interstellar medium (the gas and dust in the spaces between the stars). It would take a very long time for a new Sun to develop from the remains of our old solar system, if this is even possible.
Fortunately for us, the lifetime of our Sun is billions of years long, so we don't need to worry about the Sun's death for a very long time.
Kris