<p>This article investigates the exceptional set of the boundary for the following problem: <Equation ID="Equ29"> <EquationSource Format="TEX">\(\begin{aligned} \begin{aligned} -\frac{\partial u}{\partial t} + \mathcal {M}_{\lambda ,\Lambda }^+(D^2u) + b(x,t)\cdot Du + c(x,t)u =0 \quad \textrm{in} ~ \Omega _{T}, \end{aligned} \end{aligned}\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <mtable> <mtr> <mtd columnalign="right"> <mrow> <mtable> <mtr> <mtd columnalign="right"> <mrow> <mo>-</mo> <mfrac> <mrow> <mi>∂</mi> <mi>u</mi> </mrow> <mrow> <mi>∂</mi> <mi>t</mi> </mrow> </mfrac> <mo>+</mo> <msubsup> <mi mathvariant="script">M</mi> <mrow> <mi>λ</mi> <mo>,</mo> <mi mathvariant="normal">Λ</mi> </mrow> <mo>+</mo> </msubsup> <mrow> <mo stretchy="false">(</mo> <msup> <mi>D</mi> <mn>2</mn> </msup> <mi>u</mi> <mo stretchy="false">)</mo> </mrow> <mo>+</mo> <mi>b</mi> <mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo>·</mo> <mi>D</mi> <mi>u</mi> <mo>+</mo> <mi>c</mi> <mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mi>u</mi> <mo>=</mo> <mn>0</mn> <mspace width="1em" /> <mtext>in</mtext> <mspace width="3.33333pt" /> <msub> <mi mathvariant="normal">Ω</mi> <mi>T</mi> </msub> <mo>,</mo> </mrow> </mtd> </mtr> </mtable> </mrow> </mtd> </mtr> </mtable> </mrow> </math></EquationSource> </Equation>We provide a sufficient condition for the exceptional set in terms of the Hausdorff measure bound of this boundary portion. This condition ensures that even if the boundary values are not nonnegative on this portion, the supersolution remains nonnegative.</p>