Hi Christina

There is an advanced feature Audience visibility that can be applied at a course and program level.

The settings for this are visible to all users, enrolled users or enrolled users and members of audience. In your case the users will still be enrolled in the course and program/certification.

It is possible to unenrol users in courses by audience rule such as user has not completed a course so they are no longer a member of the audience that enrolled them in the program This would make the course not visible to the user if audience visibility is set to enrolled users . 

All of this is getting a bit complicated - the simplest way would be to rely on the course progress bars in Totara for programs and Certifications in a Block such as Current Learning that shows the courses completed and what needs to be completed

Regards