  The exact black hole solution of 2D closed string theory has, as any other
maximally extended Schwarzschild-like geometry, two asymptotically flat
spacetime domains. One can get rid of the second domain by gauging the discrete
symmetry on the SL(2,R)/U(1) coset that interchanges the two asymptotic domains
and preserves the Kruskal time orientation everywhere in the Kruskal plane.
Here it is shown that upon performing this orbifold procedure, we obtain a
theory of unoriented open and closed strings in a black hole background, with
just one asymptotically flat domain and a time-like orbifold singularity at the
origin. All of the open string states of the model are confined to the orbifold
singularity. We also discuss various physical aspects of the truncated black
hole, in particular its target duality -- the model is dual to a conventional
open string theory in the black hole geometry.
