  We study the representation theory of non-admissible simple affine vertex
algebra $L_{-5/2} (sl(4))$. We determine an explicit formula for the singular
vector of conformal weight four in the universal affine vertex algebra
$V^{-5/2} (sl(4))$, and show that it generates the maximal ideal in $V^{-5/2}
(sl(4))$. We classify irreducible $L_{-5/2} (sl(4))$--modules in the category
${\mathcal O}$, and determine the fusion rules between irreducible modules in
the category of ordinary modules $KL_{-5/2}$. It turns out that this fusion
algebra is isomorphic to the fusion algebra of $KL_{-1}$. We also prove that
$KL_{-5/2}$ is a semi-simple, rigid braided tensor category.
  In our proofs we use the notion of collapsing level for the affine
$\mathcal{W}$--algebra, and the properties of conformal embedding $gl(4)
\hookrightarrow sl(5)$ at level $k=-5/2$ from arXiv:1509.06512. We show that
$k=-5/2$ is a collapsing level with respect to the subregular nilpotent element
$f_{subreg}$, meaning that the simple quotient of the affine
$\mathcal{W}$--algebra $W^{-5/2}(sl(4), f_{subreg})$ is isomorphic to the
Heisenberg vertex algebra $M_J(1)$. We prove certain results on vanishing and
non-vanishing of cohomology for the quantum Hamiltonian reduction functor
$H_{f_{subreg}}$. It turns out that this case is much more complicated than the
case of minimal reduction.
