  A coarse compactification of a proper metric space $X$ is any
compactification of $X$ that is dominated by its Higson compactification. In
this paper we describe the maximal coarse compactification of $X$ whose corona
is of dimension $0$. In case of geodesic spaces $X$, it coincides with the
Freundenthal compactification of $X$. As an application we provide an
alternative way of extending the concept of the number of ends from finitely
generated groups to arbitrary countable groups. We present a geometric proof of
a generalization of Stallings' theorem by showing that any countable group of
two ends contains an infinite cyclic subgroup of finite index. Finally, we
define ends of arbitrary coarse spaces.
