Brain-computer interfaces (BCI) are presented as a solution for people with global paralysis, also known as locked-in syndrome (LIS). The targeted population includes the most severe patients, with no residual eye movements, who cannot use any communication device (Complete LIS). However, BCI reliability is low precisely in these cases, technical pitfalls being considered responsible so far. Here, we propose to consider also that global paralysis could have an impact on cognitive functions that are crucial for being able to control a BCI. We review a bundle of arguments about the role of motor structures in cognition. Especially, we uncover that these patients without oculomotor activity often have injuries in more 'cognitive' structures such as the frontal eye field or the midbrain, exposing them to cognitive deficits further than canonical LIS population. We develop a hypothesis about the putative role of the motor system in (covert) attention, a capacity which is a prerequisite for most BCI paradigms and which should therefore be both better assessed in patients and considered.