  We study the Dirichlet problem for an elliptic equation involving the
$1$-Laplace operator and a reaction term, namely: $$ \left\{\begin{array}{ll}
\displaystyle -\Delta_1 u =h(u)f(x)&\hbox{in }\Omega\,,\\ u=0&\hbox{on
}\partial\Omega\,, \end{array}\right. $$ where $ \Omega \subset \mathbb{R}^N$
is an open bounded set having Lipschitz boundary, $f\in L^1(\Omega)$ is
nonnegative, and $h$ is a continuous real function that may possibly blow up at
zero. We investigate optimal ranges for the data in order to obtain existence,
nonexistence and (whenever expected) uniqueness of nonnegative solutions.
