  In this paper we obtain a complete characterization of pseudo-collarable
$n$-manifolds for $n\geq 6$. This extends earlier work by Guilbault and Tinsley
to allow for manifolds with noncompact boundary. In the same way that their
work can be viewed as an extension of Siebenmann's dissertation that can be
applied to manifolds with non-stable fundamental group at infinity, our main
theorem can also be viewed as an extension of the recent Gu-Guilbault
characterization of completable $n$-manifolds in a manner that is applicable to
manifolds whose fundamental group at infinity is not peripherally stable.
