The Sun will eventually lose about half of its current mass non-linearly over several phases of post-main-sequence evolution. This mass loss will cause any surviving orbiting body to increase its semimajor axis and perhaps vary its eccentricity. Here, we use a range of solar models spanning plausible evolutionary sequences and assume isotropic mass loss to assess the possibility of escape from the Solar system. We find that the critical semimajor axis in the Solar system within which an orbiting body is guaranteed to remain bound to the dying Sun due to perturbations from stellar mass loss alone is ≈103–104 au. The fate of objects near or beyond this critical semimajor axis, such as the Oort Cloud, outer scattered disc and specific bodies such as Sedna, will significantly depend on their locations along their orbits when the Sun turns off the main sequence. These results are applicable to any exoplanetary system containing a single star with a mass, metallicity and age which are approximately equal to the Sun’s, and suggest that few extrasolar Oort Clouds could survive post-main-sequence evolution intact.