There are a couple of SF stories along this line that come to mind. The first is "A Pail of Air" by Fritz Leiber, about how a family survives for a few years after the Earth is stolen from the Sun by a dark star.
The other (the name and author of which I forget) goes roughly a) Sun suddenly collapses into a white dwarf, b) Humanity emigrates and Earth freezes, c) Earth slowly spirals in toward Sun, and d) news crew returns to record and report on the thaw and Earth's eventual demise. Title, anyone?
"For shame, gentlemen, pack your evidence a little better against another time."
-- John Dryden, "The Vindication of The Duke of Guise" 1684