  The modification of the $\phi$ meson spectrum in nuclear matter is studied in
an updated QCD sum rule analysis, taking into account recent improvements in
properly treating the chiral invariant and breaking components of four-quark
condensates. Allowing both mass and decay width to change at finite density,
the QCD sum rule analysis determines certain combinations of changes for these
parameters that satisfy the sum rules equally well. A comprehensive error
analysis, including uncertainties related to the behavior of various
condensates at linear order in density, the employed renormalization scale and
perturbative corrections of the Wilson coefficients, is used to compute the
allowed ranges of these parameter combinations. We find that the $\phi$ meson
mass shift in nuclear matter is especially sensitive to the strange sigma term
$\sigma_{sN}$, which determines the decrease of the strange quark condensate in
nuclear matter. Specifically, we obtain a linear relation between the width
$\Gamma_{\phi}$ and mass shift $\Delta m_{\phi}$ given as $ \Gamma_{\phi} =
a\Delta m_{\phi} + b\sigma_{sN}+c$ with $a = (3.947^{+0.139}_{-0.130})$, $b =
(0.936^{+0.180}_{-0.177} )$ and $c = -(7.707^{+4.791}_{-5.679}) \mathrm{MeV}$.
