We present the results of a joint XMM-Newton and NuSTAR observation (200 ks) of the galaxy cluster Abell 523 at $z=0.104$. The peculiar morphology of the cluster radio halo and its outlier position in the radio power P(1.4 GHz) - X-ray luminosity plane make it an ideal candidate for the study of radio-X-ray correlations and for the search of inverse Compton (IC) emission. We constructed thermodynamic maps derived from the XMM observations to describe in detail the physical and dynamical state of the ICM. We performed a point-to-point comparison in terms of surface brightness between the X-ray and radio emissions, to quantify their morphological discrepancies. Making use of NuSTARs hard X-ray focusing capability, we looked for IC emission both globally and locally, after modeling the purely thermal component with a multi-temperature description. The thermodynamic maps suggest the presence of a secondary merging process that could be responsible for the peculiar radio halo morphology. This hypothesis is supported by the comparison between the X-ray and radio surface brightnesses, which shows a broad intrinsic scatter and a series of outliers. The global NuSTAR spectrum can be explained by purely thermal gas emission, and there is no convincing evidence that an IC component is needed. The $3sigma$ upper limit on the IC flux in the 20-80 keV band is in the range $left[2.2 - 4.0right] times 10^{-13} , mathrm{erg} , mathrm{s}^{-1} , mathrm{cm}^{-2}$, implying a lower limit on the magnetic field strength in the range $B > [0.23 - 0.31] , mu G$. Locally, we looked for IC emission in the central region of the cluster radio halo finding a $3sigma$ upper limit on the 20-80 keV non-thermal flux of $3.17 times 10^{-14} , mathrm{erg} , mathrm{s}^{-1} , mathrm{cm}^{-2}$, corresponding to a lower limit on the magnetic field strength of $B gtrsim 0.81 , mu G$.
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