This is not the 'Star Trek' movie where, for some weird reason I'll never understand, a supernova was a catastrophic event, for civilizations with FTL travel.
If our own sun turned into a supernova (not possible btw), the nearby star wouldn't even see that for about 4 years, best case. And that would be just the radiation, matter would take hundreds, if not thousands of years to get there. So it is not like they wouldn't have any warning.
And that's for the closest star.
We are all supernova dust, after all.
A nearby supernova would definitely be sterilizing to the kind of life found on Earth, and to a lot of other imaginable forms. Of course, "nearby" in astronomical terms is sometimes unintuitive. :-)