I'm not exactly sure how an athlete can be enrolled at a school as a non-qualifier. But, apparently it's possible at some schools.
A partial qualifier can enroll, but is ineligible to participate for the first year. Provided that the player meets eligibility by the end of that first year, the player has 3 years of eligibility. If the player is 75% of the way to a degree after those 3 years of eligibility (four years in the school), the player is granted a 4th eligible year.
The partial qualifier status is when a player meets either the grades or standardized test score, but not both. It's an interesting discussion whether the partial qualifier route or the JuCo route is better for both the team and player. Many players can perform much better in the structured environment that some colleges provide (as opposed to some JuCos) and the year of acclimation and remedial coursework can help as well. From the team standpoint, the partial qualifier route is also a positive. Yet, there is a stigma associated with taking partial qualifiers that doesn't get attached to taking JuCo players, despite some of the advantages for both parties involved, which is why so many conferences have limited or eliminated partial qualifiers, but most conferences don't have similar rules on JuCo players.