Let $M$ be a smooth manifold, and $N$ be an embedded smooth submanifold of $M$ with $\partial M=\varnothing=\partial N$. Suppose, $\dim M-\dim N=1$, and $N$ is a **closed subset** of $M$.

Does the inclusion map $i: N\hookrightarrow M$ a cofibration, i.e. does this pair $(M, N)$ have homotopy extension property?

$\bullet$ I am not assuming $N$ is compact in general. In case, $N$ is compact the uniform tubular neighborhood gives positive solution.

Can someone suggest me some references?