Death feigning, sometimes designated as thanatosis, reflex immobilization, tonic immobility or faking death is generally assumed a last-resort antipredator defence, attempting to avoid being killed and consumed. Recently, faking death has also been claimed to exist with respect to sexual conflict in Odonata. Here we review a number of published cases in Anisoptera that describe how non-receptive females during oviposition escape male harassing by fleeing, plunging into vegetation, freezing immediately and remaining motionless in random body position, no longer being noted by the male hovering nearby. We argue that this reaction of the female does not match the definition of death feigning and propose a new term for it: ‘drop and stop’ behaviour. In this context it is reasoned how and under what circumstances males, if at all, are able to recognize immobile females and react to them. The adaptive value of ‘drop and stop’ is discussed and it is suggested that this behaviour in sexual conflict could have evolved from a predator avoiding tactic.