Duke said:
I don't know. I was under the impression that stars are formed out of dense gas clouds, which collapse under it's own gravity.
Perhaps similar gas clouds can be released at the death of a (large) star?
Can anyone shed some light on that?
Your right, for the most part.
The death of mid-sized stars
does release a cloud of gas, called a planetary nebula. However, these are not the giant molecular clouds that form stars. Those are called dark nebulae.
The material propelled into space at the supernova explosion of a supermassive star can trigger the gravitational collapse of a giant molecular cloud. As it collapses, it shatters into fragments, some of which can form new stars.
And what happens again to smaller stars? Don't those "just" fade out? Or explode?
We can't be entirely sure, since they burn so slowly that they last hundreds of millions of years, so none have actually burned out yet. Really small ones, those with a solar mass of less than 0.5 (i.e. half the solar mass of the Sun) are called red dwarves, they burn for hundreds of millions of years. Proxima Centauri is a red dwarf.
Most mid-sized stars (of which the Sun is an example) shed their outer layers, which become
planetary nebulae. The core of the star cools to a white dwarf and then, once it's lost all its heat, into a black dwarf.
This is how I understand it, anyway. I got confused about halfway through and had to look up a few things.
I seem to remember there being someone really good at all this astrophysics stuff, but I don't know who it was. Maybe someone can explain things a bit better.