A rotary machine, comprising: a stator assembly and a rotor assembly centered on a central axis; a magnetic bearing; and an auxiliary bearing including a first ring held in the stator assembly and a second ring delimiting a gap radially to the central axis relative to the rotor. The second ring is not rotating around the central axis in a primary operation mode and is dragged in rotation around the central axis in a secondary operation mode. The rotary machine includes a monitoring system for detecting a transition from the primary operation mode to the secondary operation mode. The monitoring system comprises a target formed on the second ring and a sensor unit fixed relative to the stator assembly. A bearing and a method for manufacturing a rotary machine are additionally disclosed.