Death of stars are fun and make for a great premise, but the actual dying of stars that are conducive to intelligent life aren't so interesting. Stars that can go supernova are too short-lived to harbour intelligent life. 

#Questions
How do you kill a star such that a civillisation is around to witness the horror of this happening and attempt to avert or escape the catastrophe?

It'll be great to have answers that consider different time-frames, 10,000 years, 100,000 years. 1 million years might be pushing it for how relatable the story can be...