  In extended supersymmetric models with a hidden sector the lightest
$R$-parity odd particle can reside in the hidden sector and act as dark matter.
We consider the case when the hidden sector has ultraweak interactions with the
visible sector. An interesting phenomenon arises if the LSP of the visible
sector is charged in which case it will decay to the hidden sector dark matter.
Due to the ultraweak interactions, the LSP of the visible sector will be
long-lived decaying outside the detector after leaving a track inside. We
investigate this possibility in the framework of a $U(1)_X$-extended MSSM/SUGRA
model with a small gauge kinetic mixing and mass mixing between the $U(1)_X$
and $U(1)_Y$ where $U(1)_Y$ is the gauge group of the hypercharge. Specifically
we investigate the case when the LSP of MSSM is a stop which decays into the
hidden sector dark matter and has a lifetime long enough to traverse the LHC
detector without decay. It is shown that such a particle can be detected at the
HL-LHC and HE-LHC as an $R$-hadron which will look like a slow moving muon with
a large transverse momentum $p_T$ and so can be detected by the track it leaves
in the inner tracker and in the muon spectrometer. Further, due to the
ultraweak couplings between the hidden sector and the MSSM fields, the dark
matter particle has a relic density arising from a combination of the
freeze-out and freeze-in mechanisms. It is found that even for the ultraweak or
feeble interactions the freeze-out contribution relative to freeze-in
contribution to the relic density is substantial to dominant, varying between
30\% to 74\% for the model points considered. It is subdominant to freeze-in
for relatively small stop masses with relatively larger stop annihilation
cross-sections and the dominant contribution to the relic density for
relatively large stop masses and relatively smaller stop annihilation
cross-sections.
