  In a recent paper, one of us studied spherically symmetric, asymptotically
flat solutions of Shape Dynamics, finding that the spatial metric has
characteristics of a wormhole - two asymptotically flat ends and a minimal-area
sphere, or `throat', in between. In this paper we investigate whether that
solution can emerge as a result of gravitational collapse of matter. With this
goal, we study the simplest kind of spherically-symmetric matter: an
infinitely-thin shell of dust. Our system can be understood as a model of a
star accreting a thin layer of matter. We solve the dynamics of the shell
exactly and find that, indeed, as it collapses, the shell leaves in its wake
the wormhole metric. In the maximal-slicing time we use for asymptotically flat
solutions, the shell only approaches the throat asymptotically and does not
cross it in a finite amount of time (as measured by a clock `at infinity').
This leaves open the possibility that a more realistic cosmological solution of
Shape Dynamics might see this crossing happening in a finite amount of time (as
measured by the change of relational/shape degrees of freedom).
