Let $L$ be an infinite regular language.
Then there exists some integer $p \ge 1$ such that any $w \in L$ with $|w| \ge p$ can be decomposed as
$$ w = xyz $$
with
$$ \begin{align*} |xy| & \le p \\ |y| & \ge 1 \\ \end{align*} $$
such that
$$ w_i = xy^iz \in L \text{ for all } i = 0,1,2,\dots $$