  Strong violations of existing fluctuation theorems may arise in
nonequilibrium steady states characterized by distributions with power-law
tails. The ratio of the probabilities of positive and negative fluctuations of
equal magnitude behaves in an anomalous nonmonotonic way [H. Touchette and
E.G.D. Cohen, Phys. Rev. E \textbf{76}, 020101(R) (2007)]. Here, we propose an
alternative definition of fluctuation relation (FR) symmetry that, in the
power-law regime, is characterized by a monotonic linear behavior. The proposal
is consistent with a large deviation-like principle. As example, it is studied
the fluctuations of the work done on a dragged particle immersed in a complex
environment able to induce power-law tails. When the environment is
characterized by spatiotemporal temperature fluctuations, distributions arising
in nonextensive statistical mechanics define the work statistics. In that
situation, we find that the FR symmetry is solely defined by the average bath
temperature. The case of a dragged particle subjected to a L\'{e}vy noise is
also analyzed in detail.
