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 H0 column densities (N
H) in the direction of the WD and at any orbital phase of the binary by modeling the continuum depression around the Lyα 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
H values follow a common course along the orbit with a minimum and maximum of a few times 1022 and 1024 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 owing 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.