  We have calculated the coherence and detectable lifetimes of synthetic
near-Earth object (NEO) families created by catastrophic disruption of a
progenitor as it suffers a very close Earth approach. The closest or slowest
approaches yield the most violent `s-class' disruption events. We found that
the average slope of the absolute magnitude (H) distribution,
$N(H)\propto10^{(0.55\pm0.04)\,H}$, for the fragments in the s-class families
is steeper than the slope of the NEO population \citep{mainzer2011} in the same
size range. The families remain coherent as statistically significant clusters
of orbits within the NEO population for an average of $\bar\tau_c =
(14.7\pm0.6)\times10^3$ years after disruption. The s-class families are
detectable with the techniques developed by \citet{fu2005} and
\citet{Schunova2012} for an average duration ($\bar\tau_{det}$) ranging from
about 2,000 to about 12,000 years for progenitors in the absolute magnitude
($H_p$) range from 20 to 13 corresponding to diameters in the range from about
0.5 to 10$\km$ respectively. The short detectability lifetime explains why zero
NEO families have been discovered to-date. Nonetheless, every tidal disruption
event of a progenitor with D$>0.5\km$ is capable of producing several million
fragments in the $1\meter$ to $10\meter$ diameter range that can contribute to
temporary local density enhancements of small NEOs in Earth's vicinity. We
expect that there are about 1,200 objects in the steady state NEO population in
this size range due to tidal disruption assuming that one $1\km$ diameter NEO
tidally disrupts at Earth every 2,500 years. These objects may be suitable
targets for asteroid retrieval missions due to their Earth-like orbits with
corresponding low $v_{\infty}$. The fragments from the tidal disruptions at
Earth have $\sim5\times$ the collision probability with Earth compared to the
background NEO population.
