  We study the formation and evolution of filamentary configurations of dark
matter haloes in voids. Our investigation uses the high-resolution LambdaCDM
simulation CosmoGrid to look for void systems resembling the VGS_31 elongated
system of three interacting galaxies that was recently discovered by the Void
Galaxy Survey (VGS) inside a large void in the SDSS galaxy redshift survey. HI
data revealed these galaxies to be embedded in a common elongated envelope,
possibly embedded in intravoid filament. In the CosmoGrid simulation we look
for systems similar to VGS_31 in mass, size and environment. We find a total of
eight such systems. For these systems, we study the distribution of neighbour
haloes, the assembly and evolution of the main haloes and the dynamical
evolution of the haloes, as well as the evolution of the large-scale structure
in which the systems are embedded. The spatial distribution of the haloes
follows that of the dark matter environment. We find that VGS_31-like systems
have a large variation in formation time, having formed between 10 Gyr ago and
the present epoch. However, the environments in which the systems are embedded
evolved resemble each other substantially. Each of the VGS_31-like systems is
embedded in an intra-void wall, that no later than z = 0.5 became the only
prominent feature in its environment. While part of the void walls retain a
rather featureless character, we find that around half of them are marked by a
pronounced and rapidly evolving substructure. Five haloes find themselves in a
tenuous filament of a few Mpc/h long inside the intra-void wall. Finally, we
compare the results to observed data from VGS_31. Our study implies that the
VGS_31 galaxies formed in the same (proto)filament, and did not meet just
recently. The diversity amongst the simulated halo systems indicates that
VGS_31 may not be typical for groups of galaxies in voids.
