[petelamana (OP)]

Last evening I attended a lecture on Cepheid variable stars.  Fascinating.  I do have several questions, which I am sure I will ask at some point during the next few days, however ...

What is the "end stage" of a Cepheid?

Once the star exhausts it He what then?


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[Janus]

It depends on what type of Cepheid you are considering.  Classical, or Type I Cepheid stars are much more massive than our Sun and Are likely to supernova ( the variable brightness is due to conditions in the outer layers and not the fusion at the core*).
Type II Cepheid stars are generally thought to be about the mass of the Sun or smaller, so they would likely end up as white dwarf stars.

* Helium in the outer layers is ionized which makes it more opaque, causing it to trap light and dim the star.  The trapped light heats the Helium causing the outer layers to expand, which allows it to cool, de-ionize, become more transparent and let more light escape,  Gravity then pulls the now cooled expanded layers back, where they reheat and the process starts all over again.