Stars must be above a certain mass to sustain nuclear fusion. If it has less than ~8% the mass of the Sun, it would be a brown dwarf, which only glows faintly from the heat of the initial gravitational collapse. And since we can detect brown dwarfs tens of light-years away, I think we can be 99.9% sure that we've detected all stars closer than that. But there may be brown dwarfs closer than Alpha Centauri that we haven't detected yet.