Spanish universities still face many barriers to the training of people with disabilities, especially with intellectual disabilities (ID). In general, continuing higher education courses are the main training response for the latter. Knowing the impact that confinement by COVID-19 has had on the students of these courses is a relevant element. The present investigation focused on analyzing the case of the confinement experience of 12 young students with ID who attended the continuing training program called Unidiversidad at the University of Alcalá (Spain). In particular, the implications on their emotional well-being, interpersonal relationships, and individual training were analyzed. Information was collected through a semi-structured interview with the students and a questionnaire with their relatives. The results reflect changes in emotional well-being linked to the increased concern of students for the health of their families. Interpersonal relationships were also affected, although participants tried to compensate for the lack of face-to-face interaction with instant messaging applications and video calls. The change in training to the online modality generated concern and uncertainty in students, although it also provided learning opportunities, which have been supported by peer tutoring and support from teachers.