  A $\Sigma^*$ state with spin-parity $J^P = 1/2^-$ with mass and width around
$1380$ MeV and $120$ MeV, refereed to as the $\Sigma^*_{1/2^-}(1380)$, has been
predicted in several pentaquark models and inferred from the analysis of CLAS
$\gamma p$ data. In the present work, we discuss how one can employ the
$\Lambda^+_c \to \eta \pi^+ \Lambda$ decay to test its existence, as well as to
study the $\Sigma^*(1385)$ state with $J^P = 3/2^+$. Because the final $\pi^+
\Lambda$ system is in a pure isospin $I = 1$ combination, the $\Lambda^+_c \to
\eta \pi^+ \Lambda$ decay can be an ideal process to study these $\Sigma^*$
resonances. In particular, we show that the decay angle and energy
distributions of the $\pi^+$ are very different for $\Sigma^*(1385)$ and
$\Sigma^*_{1/2^-}(1380)$. The proposed decay mechanism as well as the existence
of the $\Sigma^*_{1/2^-}(1380)$ state can be checked by future BESIII and Belle
experiments.
