Hundreds of millions of general anesthesia are performed each year on patients all over the world. Among these patients, 0.1–0.2% are victims of Accidental Awareness during General Anesthesia (AAGA), i.e., an unexpected awakening during a surgical procedure under general anesthesia. Although anesthesiologists try to closely monitor patients using various techniques to prevent this terrifying phenomenon, there is currently no efficient solution to accurately detect its occurrence. We propose the conception of an innovative passive brain-computer interface (BCI) based on an intention of movement to prevent AAGA. Indeed, patients typically try to move to alert the medical staff during an AAGA, only to discover that they are unable to. First, we examine the challenges of such a BCI, i.e., the lack of a trigger to facilitate when to look for an intention to move, as well as the necessity for a high classification accuracy. Then, we present a solution that incorporates Median Nerve Stimulation (MNS). We investigate the specific modulations that MNS causes in the motor cortex and confirm that they can be altered by an intention of movement. Finally, we perform experiments on 16 healthy participants to assess whether an MI-based BCI using MNS is able to generate high classification accuracies. Our results show that MNS may provide a foundation for an innovative BCI that would allow the detection of AAGA.