  We present a survey for low-ionization metal absorption line systems towards
17 QSOs at redshifts z_em=5.8-6.4. Nine of our objects were observed at high
resolution with either Keck/HIRES or Magellan/MIKE, and the remainder at
moderate resolution with Keck/ESI. The survey spans 5.3 < z_abs < 6.4 and has a
pathlength interval \Delta X=39.5, or \Delta z=8.0. In total we detect ten
systems, five of which are new discoveries. The line-of-sight number density is
consistent with the combined number density at z~3 of DLAs and sub-DLAs, which
comprise the main population of low-ionization systems at lower redshifts. This
apparent lack of evolution may occur because low ionization systems are hosted
by lower-mass halos at higher redshifts, or because the mean cross section of
low-ionization gas at a given halo mass increases with redshift due to the
higher densities and lower ionizing background. The roughly constant number
density notably contrasts with the sharp decline at z > 5.3 in the number
density of highly-ionized systems traced by C IV. The low-ionization systems at
z~6 span a similar range of velocity widths as lower-redshift sub-DLAs but have
significantly weaker lines at a given width. This implies that the
mass-metallicity relation of the host galaxies evolves towards lower
metallicities at higher redshifts. These systems lack strong Si IV and C IV,
which are common among lower-redshift DLAs and sub-DLAs. This is consistent,
however, with a similar decrease in the metallicity of the low- and
high-ionization phases, and does not necessarily indicate a lack of nearby,
highly-ionized gas. The high number density of low-ionization systems at z~6
suggests that we may be detecting galaxies below the current limits of
i-dropout and Ly-alpha emission galaxy surveys. These systems may therefore be
the first direct probes of the `typical' galaxies responsible for hydrogen
reionization.
