This can be controlled in your settings.  Ideally, when you set up your ILTs you want to go to the Course Properties → Advanced Properties → Catalog Options and set this before your ILT’s are published.

Under your Self-Enrollment options, you need to set the “end date” of the self-enrollments as the date of the last available session.  This will allow for users to still enroll on the date of the session (unless you want to make the cut off earlier!) but will not allow them to enroll after that date.  I always do this so that even if it takes me a few days to go back and “close out” any details on ILTs, I don’t have to worry about additional users enrolling.

This does not, however, automatically make the course “invisible” to users, but it will “lock” the course so that users cannot continue to enroll in it.  To make the course no longer visible to users who were not enrolled, you can go back into the same section of the course properties after the course is over and change the course visibility to “Show the course only to enrolled users” OR you can remove the course from all catalogs, which effectively does the same thing - only enrolled users would still see the course.

Thank you so much for your help on this trose23!!