In this paper we study the factors that influence both dropout and (4-year) degree completion throughout university by applying the set of discrete-time methods for competing risks in event history analysis, as described in Scott and Kennedy (2005). In the French-speaking Belgian community, participation rates are very high given that higher education is largely financed through public funds, but at the same time, the system performs very poorly in terms of degree completion. In this particular context, we explore two main questions. First, to what extent is socioeconomic background still a determinant of success for academic careers in a system that, by construction, aims to eliminate economic barriers to higher education? Second, given the high proportion of students who fail their first year and are unable to move to their second year, can authorities promote degree completion and decrease dropout among students who have already experienced a failure? Using the competing risks model, we show that in spite of low entry barriers, students coming from lower socioeconomic background are more vulnerable to dropout along the whole academic path because of financial constraints that prevent them from re-enrolling. Also, our results reveal that, after a failed year, a significantly higher proportion of students who re-enroll in a different field obtain a degree compared to those that re-enroll in the same field, suggesting that universities should rethink the mechanisms available to manage failure and guide student choices.