  Accretion of mass onto a white dwarf (WD) in a binary system can lead to
stellar explosions. If a WD accretes from stellar wind of a distant evolved
giant in a symbiotic binary, it can undergo occasional outbursts in which it
brightens by several magnitudes, produces a low- and high-velocity
mass-outflow, and, in some cases, ejects bipolar jets. In this paper, we
complement the current picture of these outbursts by the transient emergence of
a neutral region in the orbital plane of symbiotic binaries consisting of wind
from the giant. We prove its presence by determining H$^0$ column densities
($N_{\rm H}$) in the direction of the WD and at any orbital phase of the binary
by modeling the continuum depression around the Ly$\alpha$ line caused by
Rayleigh scattering on atomic hydrogen for all suitable objects, i.e.,
eclipsing symbiotic binaries, for which a well-defined ultraviolet spectrum
from an outburst is available. The $N_{\rm H}$ values follow a common course
along the orbit with a minimum and maximum of a few times $10^{22}$ and
$10^{24}$ cm$^{-2}$ around the superior and inferior conjunction of the giant,
respectively. Its asymmetry implies an asymmetric density distribution of the
wind from the giant in the orbital plane with respect to the binary axis. The
neutral wind is observable in the orbital plane due to the formation of a dense
disk-like structure around the WD during outbursts, which blocks ionizing
radiation from the central burning WD in the orbital plane.
