  The under-abundance of asteroids on orbits with small perihelion distances
suggests that thermally-driven disruption may be an important process in the
removal of rocky bodies in the Solar System. Here we report our study of how
the debris streams arise from possible thermally-driven disruptions in the
near-Sun region. We calculate that a small body with a diameter $\gtrsim0.5$ km
can produce a sufficient amount of material to allow the detection of the
debris at the Earth as meteor showers, and that bodies at such sizes thermally
disrupt every $\sim2$ kyrs. We also find that objects from the inner parts of
the asteroid belt are more likely to become Sun-approacher than those from the
outer parts. We simulate the formation and evolution of the debris streams
produced from a set of synthetic disrupting asteroids drawn from Granvik et al.
(2016)'s near-Earth object population model, and find that they evolve 10--70
times faster than streams produced at ordinary solar distances. We compare the
simulation results to a catalog of known meteor showers on Sun-approaching
orbits. We show that there is a clear overabundance of Sun-approaching meteor
showers, which is best explained by a combining effect of comet contamination
and an extended disintegration phase that lasts up to a few kyrs. We suggest
that a few asteroid-like Sun-approaching objects that brighten significantly at
their perihelion passages could, in fact, be disrupting asteroids. An extended
period of thermal disruption may also explain the widespread detection of
transiting debris in exoplanetary systems. Data and codes that generate the
figures and main results of this work are publicly available on
10.5281/zenodo.2547298 and https://github.com/Yeqzids/near-sun-disruptions.
