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Presumably they would know enough about stellar evolution to know that the star could die at "any moment." Certainly the habitable zone of the system would have been moving outward away from the star for long enough (millions of years) by then that unless they were already moving the planet or had already abandoned it, they wouldn't be around anymore anyway.
The sort of explosion you're talking about, unless I'm mistaken, tends to happen around highly massive stars which don't spend a lot of time on the main sequence, so there would be the problem of "Is your star likely to live long enough for life to develop around its planets anyway?" It sounds like the answer is "no." But that aside, there's various stages of fusion that massive stars go through, and it should be possible for a sufficiently advanced civilization to determine where it's star is on this process. For example, when our sun, which currently fuses hydrogen into helium, starts fusing helium into into carbon, it will undergo a catastrophic event (from the perspective of life on its planets) called the
helium flash. Higher mass stars would experience these as well,
lots of them, as helium is fused in the shells around the core.
One can probably use asteroseismology to determine which stage of fusion their star is at. Once a star reaches silicon fusion, you've got about a week before the star submits to a
core collapse supernova.
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