Interestingly, WD 0806-661B orbits a white dwarf star (called, unsurprisingly, WD 0806-661) and could be considered an exoplanet. But it orbits at a huge distance: 2,500 AU - or 2,500 times the distance between the sun and Earth. For it to be a planet, it would need to be orbiting far, far closer to the white dwarf.
However, there is another possibility. This white dwarf star was once a star two-times the mass of our sun. White dwarfs are what remains of an old star after it has run out of fuel and died.
Indeed, our sun has a similar fate in approximately 4 billion years time. After it has run out of hydrogen fuel, puffed up as an angry "red giant" and swallowed the Earth as it expands, our red giant sun will eject its outer layers, leaving a white dwarf shining in the core of the resulting "planetary nebula." (I've written about this fascinating scenario before: "What Will Happen When the Sun Turns into a White Dwarf?")
Models predict that once the sun has shed huge quantities of mass after its red giant phase, the remaining planets of the solar systems will drift into wider orbits. Is this what happened to WD 0806-661B? Was it once a very massive planet orbiting a star twice the mass of the sun? Further measurements of the object are obviously needed.