An elevator safety supervising entity (SSE) includes a car safety supervising unit (SSU) controlling functions of car safety components and having at least one car sensor sensing car-related parameters, a head SSU controlling functions of shaft safety components and having at least one shaft sensor sensing shaft-related parameters, and a data linkage transmitting signal data between the SSUs. Both SSUs detect a failure in the other one of the SSUs and in the data linkage signal data transmission and in response switch from a normal operation mode to a failure operation mode. In the failure operation mode, the SSUs operate autonomously to keep the elevator operative at least temporarily with a sufficiently high safety even when functions of the elevator SSE are disturbed due to failures and e.g. passengers may be evacuated from the elevator car before completely stopping elevator operation.