  We present a study of the faint-end of the X-ray Luminosity Function of Low
Mass X-ray binaries in the Globular Cluster system of the cD galaxy NGC 1399 by
performing a stacking experiment on 618 X-ray undetected GCs, in order to
verify the presence of faint LMXBs and to constrain the faint-end slope of the
GC-LMXBs XLF below the individual detection threshold of $8\times10^{37}$ erg
s$^{-1}$ in the $0.5-8$ keV band. We obtain a significant X-ray detection for
the whole GC sample, as well as for the red and blue GC subpopulations,
corresponding to an average luminosity per GC $<L_{X}>_{GC}$ of
$(3.6\pm1.0)\times10^{36}\ erg\ s^{-1}$, $(6.9\pm2.1)\times10^{36}\ erg\
s^{-1}$ and $(1.7\pm0.9)\times10^{36}\ erg\ s^{-1}$, respectively for all, red
and blue GCs. If LMXBs in red and blue GCs have the same average intrinsic
luminosity, we derive a red/blu ratio $\simeq 3$ of GCs hosting LMXBs
($2.5\pm1.0$ or $4.1\pm2.5$ depending on the surveyed region); alternatively,
assuming the fractions observed for brighter sources, we measure an average
X-ray luminosity of $L_{X}=(4.3\pm1.3)\times10^{37}\ erg\ s^{-1}$ and
$L_{X}=(3.4\pm1.7)\times10^{37}\ erg\ s^{-1}$ per red and blue GC-LMXBs
respectively. In the assumption that the XLF follows a power-law distribution,
we find that a low-luminosity break is required at $L_{X}\leq 8\times10^{37}$
erg s$^{-1}$ both in the whole, as well as in the color-selected (red and blue)
subsamples. Given the bright-end slopes measured above the X-ray completeness
limit, this result is significant at $>3\sigma$ level. Our best estimates for
the faint end slope are $\beta_{L}=-1.39/-1.38/-1.36$ for all/red/blue
GC-LMXBs. We also find evidence that the luminosity function becomes steeper at
luminosities $L_X\gtrsim 3\times 10^{39}$ erg s$^{-1}$, as observed in old
ellipticals.
