  Using a semi-analytic method calibrated to the global star formation history
and the stellar mass function at $z=0$, we attempt to understand the most
stellar deficient galaxy groups. We argue such groups are a kind of fossil
group (FGs) -- in comparison to the normal groups of galaxies, they assemble
both halo and stellar mass earlier. We find there is a central galaxy and
satellite conformity between these FGs and normal groups: centrals and
satellites in the former form earlier and more stellar deficient than their
counterparts of the latter. We term this effect "Assembly Conformity" of dark
matter halos. This effect accounts for about 70 percent of the difference in
stellar content between FGs and normal groups. When split by the peak redshift
for the star formation rate of a group, the mass functions of satellite halos
on either side of the peak redshift are found to be indistinguishable between
FGs and normal groups, indicating a self-similarity of halo assembly with
respect to the peak. The "baryonic environmental" effect due to ram-pressure
and gas heating accounts for about 30 percent of the difference in stellar
content. While the total stellar mass of FGs is lower than that of normal
groups, we predict that the mass of the brightest central galaxy of FGs is, on
average, higher than that of normal groups. We also predict that in the central
galaxies of FGs, there is a negative stellar age gradient from the center
outward, where the opposite is expected for those in normal groups.
