  The $\phi$-meson properties in cold nuclear matter are investigated by
implementing resonant $\phi N$ interactions as described in effective
approaches including the unitarization of scattering amplitudes. Several
$N^*$-like states are dynamically generated in these models around $2$ GeV, in
the vicinity of the $\phi N$ threshold. We find that both these states and the
non-resonant part of the amplitude contribute sizably to the $\phi$ collisional
self-energy at finite nuclear density. These contributions are of a similar
strength as the widely studied medium effects from the $\bar K K$ cloud.
Depending on model details (position of the resonances and strength of the
coupling to $\phi N$) we report a $\phi$ broadening up to about $40$-$50$ MeV,
to be added to the $\phi\to\bar K K$ in-medium decay width, and an attractive
optical potential at threshold up to about $35$ MeV at normal matter density.
The $\phi$ spectral function develops a double peak structure as a consequence
of the mixing of resonance-hole modes with the $\phi$ quasi-particle peak. The
former results point in the direction of making up for missing absorption as
reported in $\phi$ nuclear production experiments.
