The presented text has a basic aim to highlight one of the pressing problems of higher educational system in the Czech Republic, which is the question of unsuccessful graduation due to the decision of an institution or at own request of a student. The authors present the key context of the phenomenon in relation to the Czech Republic and the particular university with the aim to demonstrate some specific aspects of applied research project, which has a great importance in many structural dimensions in higher educational system. The qualitatively oriented study wants to demonstrate a pedagogical intervention as a concrete form of mechanism of equal opportunities. The authors have long-term pedagogical experience, and also experience in development and research field of higher education of students with specific educational needs. They want to emphasize that the support for the target groups of students can be optimally corrected (with respect to the conditions of universities, the relevant field of study, individualities of students, etc.), if the final research findings are correctly and exactly defined.