How does understanding the affects that will occur if our sun disappears help us prepare for this outcome?
Without the sun the earth would be a frozen planet in the first year so the only way to survive such temperatures would be to get as close to the core as possible.
We would not be able to breathe because solar energy is turned into oxygen through plants, but good news is that we would still be able to breathe for the first 1000 years because there would be enough oxygen to last us the first 1000 years on earth, after that we would all die.
At first, we would not notice for the first 8 light minutes (light minutes are the distance light can travel in a minute. We would not be in the gravitational pull of the sun and start flying around in space in a straight line.
When the sun burns out earth would be cold enough to freeze the top layer of the ocean but creatures that live deep under water won’t have a problem.
In order to survive we would need to dig as close to the earths core as possible and start a civilization there, or we would need to find a way to live at the bottom of the ocean without our bodies being compressed into nothing.