How many naked-eye stars have 'died' since they emitted the light we are seeing?

Question

This question is sort of in the spirit of this xkcd:

The light we get from stars was emitted many years in the past, but the distances to stars which are bright enough to be visible to the naked eye are not that great, so the light we received likely wasn't emitted long enough ago that the stars would have undertaken significant changes.

On the other hand, some bright stars are red giants, which are very bright, very far away, and pretty close to the end of their lives, so there is a higher chance that they have collapsed in the meantime.

So: what numerical fraction of stars which are visible by naked eye are likely to have undertaken significant steps in their stellar evolution? Here I'm interested both in main-sequence stars evolving into red giants, giants undergoing collapse, and similar events. Similarly, how does this answer change if you increase the range to stars that are visible using a reasonable pair of binoculars?

In case special relativistic effects are important, for the purposes of this thread, both the current frame of reference of the solar system and the rest frame of the galaxy are interesting.

Answer 1

There are about 10,000 naked-eye stars (likely optimistic). Typical distances are less than a kiloparsec (3000 light-years, see for example post by @RobJeffries). Red-Giants (RG) still have a lifetime of about 10 Million years*, so only something like $10^{-4}$ would have already "died"... which means even if every single naked-eye star were a RG, only about 1 of those 10,000 would likely have already died. So the answer is probably 0-1 stars.

Since the list of naked-eye (ish) stars is compiled, it wouldn't be too hard to just go through and see which (if any) have a non-negligible probability of having died... would be a good class project for someone! This, of course, completely neglects binarity... which is hard to model, even in detail. Naively, I think binaries are more likely to extend lifetimes than shorten them, however - so that probably makes this estimate even more optimistic.

In regards to the change from using Binoculars instead: again this could be explored using the above-linked catalog but I suspect @DavidHammen is right (in the comments above) - that the bulk of stars that become visible with Binoculars are low-mass dwarfs, decreasing the fraction of likely-to-have-died-visible-stars, and negligibly increasing the total expected number of dead stars.

*Regarding RG lifetime, I'm not finding any great sources for lifetimes, but 10 Myr is the number of remember offhand. It looks like that might be on the lower end---again making this estimate more optimistic.