The pandemic emergency of the coronavirus disease 2019 (COVID-19) shed light on the need for innovative aids, devices and assistive technologies to enable people with severe disabilities to live their daily lives. EEG-based Brain-Computer Interfaces (BCIs) can lead individuals with significant health challenges to improve their independence, facilitate participation in activities, thus enhancing overall well-being and preventing impairments. This systematic review provides state-of-the-art applications of EEG-based BCIs, particularly those using motor-imagery (MI) data, to wheelchair control and movement. It presents a thorough examination of the different studies conducted since 2010, focusing on the algorithm analysis, features extraction, features selection and classification techniques used, and wheelchair components and performance evaluation. The results provided in this paper could highlight the limitations of current biomedical instrumentations applied to people with severe disabilities in the pandemic context of Covid-19 and bring focus to innovative research topics.