So let $f(z)$ by a density function for $z\in\operatorname{supp}f$. In some cases (for example when $f$ is the pdf of the normal distribution), $\operatorname{supp}f$ will be $\mathbb{R}$ and one could write:
$$\lim_{z\to+\infty}f(z)=c$$
but how do you translate the limit '$\lim_{z\to+\infty}$' to situations where where $\operatorname{supp}f$ is not $\mathbb{R}$ and you want describe the behaviour of $f(z)$ as $z$ goes to the upper limit of $\operatorname{supp}f$?
You can let $M=\sup\text{supp} f$ (the supremum of the support of $f$). This is the smallest number that is larger than all elements of the support.
Then you can consider the limit
$$\lim_{z\rightarrow M^-} f(z),$$
where the minus sign indicates that I'm only considering the limit from the left.