A white dwarf is a star that has stopped fusion, so you remain with a massive iron core. It still emits light because of the heat it contains and it takes billions of years for the heat to dissipate. As you know, the earth's core is iron and is still fluid from all the energy it packed from all the collisions with asteroids, even after a couple BILLION years.
The iron cores left behind by white dwarfs are much bigger than the earth's core, so it'll take many, many billions of years for the heat to dissipate into space.
Eventually, the remains of a white dwarf will cool down until it emits no more light and you'll just have an iron core floating in space. After mergers with other galaxies, nearby supernovaes or passing rogue stars/planets and so on, these extinct stars may change course, become rogue "black dwarfs" and perhaps even join other solar systems to become planets.
Extinct white dwarfs have not yet been observed, mainly because they haven't had enough time to cool down and once they do cool down, it's very difficult to observe them in space. But large iron cores floating in space remain pretty much that, unless they are swallowed by a black hole, other stars or collide with other very large objects in space. Have a look at the planet mercury for example, that is pretty much a floating iron ball in space and that is what it will remain until something else swallows it up.
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A white dwarf star is either a helium white dwarf formed from a red dwarf (none exist yet) or basically a large lump of carbon. A white dwarf will cool over billions of years and become a black dwarf They are definitely not iron, nor are they degenerate matter - that is a neutron star. The extremely hot carbon may crystallize and form a giant diamond. Our sun will eventually become a white dwarf