This can be done by using the gathered
environment, like this example with a curly bracket (brace):
\documentclass[a4paper,12pt]{article}
\usepackage{amsmath}
\begin{document}
$\left\{
\begin{gathered}
\mathrm{x} \\
\mathrm{y} \\
\mathrm{z} \\
\end{gathered}
\right.$
\quad
$\left\{
\begin{gathered}
x \\
y \\
z \\
\end{gathered}
\right.$
\end{document}
I can’t remember where I found this, but it was on a forum explaining how to do one bracket with multiple lines of text inside it.