There have been theories that a hidden, dead star (named [Nemesis](https://en.wikipedia.org/wiki/Nemesis_(hypothetical_star))) orbits our solar system far beyond the Oort cloud.  Such hypotheses generally assume that Nemesis is now in the form of either a red or a brown dwarf due to the limiting constraint that we cannot see it.  And, realistically, even if it _were_ still burning, it would _probably_ be too far away to look like a 'second sun' without being so massive that it would destabilize our main sun's planets' orbits.  In all likelihood, Nemesis would be seen as a very bright star.  
But such a star would, even then, have pretty bad implications for the stability of our solar system's planets' orbits as previously stated.  That is, in fact, one of the things that _led_ to the 'Nemesis' hypothesis; apparently, a [periodicity](https://en.wikipedia.org/wiki/Extinction_event#Patterns_in_frequency) has been been observed in the frequency extinction events, and this _could_ be explained by periodic meteor bombardments caused by a distant massive object mucking with the orbits of comets and sending them spiraling in toward the inner planets.