  Singular Finsler metrics, such as Kropina metrics and $m$-Kropina metrics,
have a lot of applications in the real world. In this paper, we study a class
of singular Finsler metrics defined by a Riemann metric $\alpha$ and 1-form
$\beta$ and characterize those which are respectively Douglasian and locally
projectively flat in dimension $n\ge 3$ by some equations. Our study shows that
the main class induced is an $m$-Kropina metric plus a linear part on $\beta$.
For this class with $m\ne -1$, the local structure of projectively flat case is
determined, and it is proved that a Douglas $m$-Kropina metric must be
Berwaldian and a projectively flat $m$-Kropina metric must be locally
Minkowskian. It indicates that the singular case is quite different from the
regular one.
