That is not accurate for all stars. Our star, for instance, is a yellow dwarf star (Type G Main Sequence). When it runs out of fuel it will briefly swell up as a red giant then collapse into a white dwarf. At no point will it explode because it simply lacks the mass for that type of chain reaction. We have a billion years before this happens, so can literally fly existing rockets elsewhere if need be. A billion years is a long time.