  We study the gapped phase of Kitaev's honeycomb model (a Z_2 spin liquid) in
the presence of lattice defects. We find that some dislocations and bond
defects carry unpaired Majorana fermions. Physical excitations associated with
these defects are (complex) fermion modes made out of two (real) Majorana
fermions connected by a Z_2 gauge string. The quantum state of these modes is
robust against local noise and can be changed by winding a Z_2 vortex around a
dislocation. The exact solution respects gauge invariance and reveals a crucial
role of the gauge field in the physics of Majorana modes.
