I don’t understand this. It seems to assume there’s still some gravitational center to the solar system with the sun gone, because the Earth’s orbit altering is only mentioned after hundreds of years. No, when the sun disappears, all of the planets shoot off onto their merry ways. The tiniest chance that Earth is eventually captured by Jupiter might mean some form of life re-evolves in the oceans (The Age of Tardigrades!), but (a) the odds of this are vanishingly small, and (b) humans would be long dead by then.

Also, humans surviving in bunkers? For years? The Earth has a nice, hot core, but unless you live near an active volcano, no bunker is nearly deep enough to benefit from that heat. And I suspect that the numbing cold would cool the surface enough to extinguish most of the active volcanos. Bunkers will be surrounded by deeply frozen earth, as hard as concrete, within a year. If your bunker is hooked up to a nuclear reactor, you might run heaters enough to stay warm; everyone else is a corpsicle.

If the sun disappears, all humans are extinct within a year.

This was put together by an AI, or a teenager with an overactive imagination.