Motivated by the observations of electron holes (EHs) strongly correlated with VLF saucers, the basic idea explored here is that when the parallel potential drop in a developing diverging electrostatic shock encounters a localized density cavity, a set of plasma processes are triggered including (i) formation of an upward-moving double layer (DL), (ii) setting up of potential gradients in which counterstreaming of electrons occurs on the DL's high-potential side, and (iii) generation of wave packets containing linear and nonlinear waves, such as the EHs. We specifically examine here the temporal and spatial evolution of such wave packets (WPs) in a one-dimensional Vlasov simulation. If such evolution persists in multi-dimensional treatments, the frequency dependent angular dispersion of the WPs could generate VLF saucers. A rapid growth of the wave packets to large amplitudes within a distance of about hundred Debye lengths gives an effective mechanism for the localization of the source for the saucers. Estimates show that the electrostatic energy stored in a wave packet containing just a few large-amplitude EHs is sufficient to power typical VLF saucer events.