The formation of the electron energy distribution function (EEDF) and phase flows of electrons in the plasma of a positive column of a glow discharge in a model gas with strong vibrational excitation, similar to molecular nitrogen, is analyzed in a wide pressure range. It is found that the traditional local approximation for calculating the EEDF can only be used at medium gas pressures, when the characteristic size of the plasma volume exceeds electron energy relaxation length in the entire range of electron energies. With a decrease in gas pressure, a new phenomenon is discovered—merging the phase flow streamlines into a single line on the coordinate-energy phase plane in the energy region of the of vibrational excitation threshold. It is shown that the combination of a strong electron sink at the threshold of vibrational excitation and the deceleration of electrons in an ambipolar field lead to a practical ‘vanishing’ of the component of the phase electron flux upward in energy. As a result, the streamlines of electron phase flow approach to some approximately straight line of constant kinetic energy close to the threshold energy of vibrational excitation. The formation of this feature on the phase plane correlates with the predominant escape to the walls of electrons with kinetic energy equal to the threshold of vibrational excitation.