  The main goal of this work is to pursue an investigation of cosmic string
configurations focusing on possible consequences of the Lorentz-symmetry
breaking by a background vector. We analyze the possibility of cosmic strings
as a viable source for fermionic Cold Dark Matter particles. Whenever the
latter are charged and have mass of the order of $10^{13}GeV$, we propose they
could decay into usual cosmic rays. We have also contemplated the sector of
neutral particles generated in our model. Indeed, being neutral, these
particles are hard to be detected; however, by virtue of the Lorentz-symmetry
breaking background vector, it is possible that they may present an
electromagnetic interaction with a significant magnetic moment.
