A landing bearing assembly for a rotary machine rotatable around a central axis and having a stator, a rotor with a shaft, a magnetic bearing, an auxiliary rolling bearing with two lateral faces, a landing sleeve facing, in normal operation of the rotary machine when the rotor is supported only by the magnetic bearing, the auxiliary rolling bearing at a nominal distance defined as the landing airgap El, the auxiliary rolling bearing coming into contact with the landing sleeve upon landing of the rotor in the event of a high shock. The assembly further provides a compliance ring with a nominal thickness Eo made from a material with a lower mechanical stiffness than the material constituting the other components of the landing bearing assembly to first absorb some energy of the shock by elastic deformation resulting in a reduction of its thickness.