If the Sun would simply disappear now we would not know this until only after 8 minutes. Light and gravity are propagates with the speed of light. We would float adrift throughout the Milky Way and the light we would get from the stars would be 1/300 of the light we get now form the Moon.
By the end of the first week without the Sun we would have freezing temps. After 1 year we would have -100 F degrees. Plants would have been long gone, but we would still have oxygen for thousands of years.
In more than a year the air will freeze and fall as snow because the temperatures would be so low that the oxygen would become liquid. Since the oceans will freeze the liquid water would still exist at the bottom of the oceans and many animals would still live in there. The bacteria will live just fine.
Geothermal heat would last for billions of years, so if you secure a good place in a warm underground community you could still have a good life. So, there is always a solution. In any case, Sun don’t leave us.