  We analyse the trapping of eigenspinors of the charge conjugation operator
with dual helicity (Elko), in thin and thick string-like models with
codimension-2. Elko spinor fields describe mass dimension one fermions in four
dimensions (and, correspondingly, mass dimension two fermions in six
dimensions), that represent natural dark matter prime candidates. This dark
spinor has many applications, from particle physics to cosmology. On the other
hand, six-dimensional brane-world models have, among other prominent features,
the spontaneous confinement of free spin 1 fields and a mechanism that explains
the mass hierarchy of fundamental fermions. In this paper, we use scalar
couplings in order to confine the zero mode of Elko in six dimensions.
Moreover, we use the Elko dark spinor features to propose an exotic coupling in
order to remove the complex-valued terms in the massive Kaluza-Klein modes.
Hence, we show that six dimensional models can resolve the main issues of Elko
fields confinement presented in five dimensions.
