  We construct models of two exotic objects: (i) a wormhole whose throat is
hidden by a stellar object like a neutron star; and (ii) a wormhole inside a
black hole. We work within Einstein's gravity coupled to two scalar fields with
a specific choice of the scalar field Lagrangian. In general, the model
contains ghosts, but they are eliminated using the constraints given by the
Lagrange multiplier fields. The constraints are a generalization of the mimetic
constraint, where non-dynamical dark matter effectively appears. As a result,
in our model, instead of the non-dynamical dark matter, non-dynamical exotic
matter like a phantom effectively arises. For the mixed wormhole-plus-star
system, we find the corresponding mass-radius relations and show that it is
possible to get characteristics comparable to those of ordinary neutron stars.
For the wormhole inside the black hole, we find an extremal limit where the
radius of the throat coincides with the radius of the event horizon and
demonstrate that the Hawking temperature vanishes in this limit.
