Granvik et al. (2016, hereafter G16) reported that dynamical models of the near-Earth asteroid (NEA) population predict more bodies with perihelia near the Sun than can be accounted for by observations, and proposed that low-perihelion NEAs undergo 'supercatastrophic disruption' (SCD) by an unknown process. Here we examine this hypothesis and extend it to include other low-perihelion bodies such as SOHO comets and meter- and millimeter-sized meteoroids. We find that no NEAs with well-known orbits have crossed inside the G16 limit (~0.08 AU or 16 solar radii) in the last 104 years, providing indirect support for their hypothesis. Asteroid (467372) 2004 LG is an exception. Having spent 2500 years within the G16 limit in the near past, it poses a challenge to SCD. We report that ungrouped SOHO comets show an excess of orbits in the ecliptic plane, and appear at rates consistent with their being small (25 m class) asteroids undergoing SCD, rather than true comets. We find that there is an abundance of millimeter-sized meteoroids inside the G16 limit even when cometary contamination is accounted for, but there are no meter-sized fireballs with known orbits that have perihelia inside even 0.3 AU. The SCD process then doesn't produce meter-sized chunks but may produce abundant millimeter-sized particles. We propose that meteoroid impacts, which reach high speeds and number densities in the near-Sun region, could explain the SCD process as well as contributing both to the unusual light curves of and to the destruction of SOHO comets.