A low-energy enhancement of radiative strength functions was observed in experiment in several mass regions of nuclei, and it is believed to impact considerably the calculated neutron-capture rates. In the shell-model framework it was demonstrated to be possibly due to the magnetic dipole radiation. Up to now, the M1 deexcitation strength function was described within this framework in the mid-mass nuclei from the pf and pfg shells (e.g., Sc44,Cr50,Fe56,57,60,66,68,Ni59,60,70,Mo94–96,Zr90), indicating systematically the presence of an up-bend at low energy. Therefore, the enhancement was accepted as a robust feature of the radiative decay. However, its exact magnitude and regions of emergence in the nuclear chart are still to be characterized in microscopic calculations. In this work, for the first time, the low-energy behavior of the radiative M1 strength in heavier nuclei, which can be described in the g7/2d5/2,3/2s1/2h11/2 shell, is investigated. The enhancement of the M1 deexcitation strength around N=80 is confirmed, and is similar to that found previously in lighter nuclei. In contrast, no such up-bend is present on the proton drip line, in the deformed N=Z=54Xe108 nucleus. From analysis of calculated magnetic dipole strengths the orbital nature of the observed enhancement is suggested. Photoemission and photoabsorption distributions on selected states are compared and the impact of different uncertainties in the theoretical treatment on the magnitude of M1 strengths at low photon energies is discussed.