  This article investigates the exceptional set of the boundary for the
following problem: \begin{equation*} \begin{aligned} -\frac{\partial
u}{\partial t} + \mathcal{M}_{\lambda,\Lambda}^+(D^2u) + b(x,t)\cdot Du +
c(x,t)u =0 \quad \rm{in} ~ \Omega_{T}, \end{aligned} \end{equation*} We provide
a sufficient condition on the exceptional set in terms of the bound of the
Hausdorff measure of this boundary portion. This condition ensures that even if
the boundary values are not nonnegative on this portion, the supersolution
remains nonnegative.
