How to avoid a MCU to run constantly when a superheterodyne radio receiver is receiving nothing, and possibly enter in deep sleep?
A superhet receiver won't invent signal to the same degree but you still have the problem of power drawn by the receiver itself. Radio links that don't have one end mains powered typically need careful efforts to establish a schedule of check-in appointments and suffer a latency in that a message may not be able to be sent until the next scheduled opportunity. 

This is not a problem which has a general solution, rather only a variety of ways the task can be reduced to something that is solvable, such as mains power, time schedules, or ranges short enough for passive receivers to work.