This is fairly common in India in private institutions, especially professional schools such as for Engineering, Medicine, Dentistry and Business Administration.
A certain percentage of places are designated 'Management Quota', i.e., the management is free to do with them as it wishes. They are used in many ways. For example, if a certain religious community/sect/order runs the place, it may set aside a large chunk of the management quota to admit students from its community/sect/order; if a (non-sectarian) charitable trust runs the place, as is very common, it may set aside some percentage of the management quota for indigent students who would otherwise not had the chance to attend the institution. Additionally, almost invariably, some part of the management quota is sold to the highest bidder in a pure cash transaction. In this way, rich students end up subsidizing a reasonable number of otherwise deserving students.
There is a significant number of (relatively much less deserving) candidates that all institutions (private or public) are required to admit, such as those coming from the so-called "Scheduled Castes", "Scheduled Tribes", "Other Backward Classes" (from communities that have been lagging in privilege and access to economic opportunities because of their caste/religion), and candidates that have done most of their prior schooling in (massively underserved) rural areas (IOTW, "Reservation" aka Affirmative Action candidates). In fact, the chunk of places allotted (by Government Order) to Affirmative Action candidates is much larger than Management Quota, and even 'Merit Quota' (i.e., candidates who sit competitive examinations in order to gain admission).
As far as subsequent success is concerned, though, it's sink-or-swim for all the candidates who are admitted: they are not given any preference in tests, exams, etc. In some specific cases, for a small initial period, affirmative action candidates may be allowed to advance with lower scores, but that is very much a small exception, not the norm.