  Coning off a collection of uniformly quasiconvex subsets of a Gromov
hyperbolic space leaves a new space, called the cone-off. Kapovich and Rafi
generalized work of Bowditch to show this space is still Gromov hyperbolic. We
show that the Gromov boundary of cone-off embeds in the boundary of the
original hyperbolic space. (A stronger version of this result was previously
obtained by Dowdall and Taylor; see Note in text.) Moreover, under some
acylindricity assumptions we give a precise description of the image. As an
application, we are able to characterize the elliptic and loxodromic elements
of groups acting on certain cone-offs of acylindrical actions.
