I'm afraid there are no 'wild star cores' in the Solar System backyard. A supernova remnant would either be a white dwarf, or a city-sized neutron star (possibl

I'm afraid there are no 'wild star cores' in the Solar System backyard. A supernova remnant would either be a white dwarf, or a city-sized neutron star (possibly a black hole) with a mass larger than that of the Sun. The latter could go undetected, but can be safely excluded since in that case it would be the Solar System actually orbiting it (or anyway being affected by it - the minimum mass for a neutron star is ~1.4 Sol, and a black hole would be even larger), and we already know the Sun's path around the Milky Way to a certain extent. OTOH a white dwarf would likely take billions of years to cool off and we would be able to spot it - so no, only planetary bodies may still be lurking there undetected. Edit - clarification.