At the close of each registration period, each chair receives a printout showing enrollment numbers for the courses being offered. Problems are of two kinds: over-enrollment and under-enrollment. The Dean and Registrar monitor course enrollments, and will contact you if they notice red flags. Here are the ways these problems are typically dealt with.
Each faculty member with an over-enrolled course will receive a copy of the roster and wait list from the registrar. Sometimes, a bidding tie means that there is no clear candidate for the last spot(s) in the course. In this instance, the faculty member can note a preference for which tied students to let into the course; otherwise, the registrar will use a randomized process to make the selection. Students who are excluded will add a course during Accommodation Evening.
As Chair, you have several options for managing over-enrollments, and should be in touch with the Registrar should you choose any of these:
Ask the teacher whether s/he would be willing to let in another student. This is only feasible if the number over-enrolled is relatively small, and the designated classroom, if applicable, has sufficient space. Discourage over-eager faculty from letting in too many students (often a temptation for untenured faculty), as too big a class is often not good for the overall quality of the course from both the student and teacher perspective. By legislation, the course cap may be "exceeded by no more than four students" (see the Faculty Handbook).
Keep the course cap as originally set. If the course is severely over-enrolled, speak with the Dean and Registrar about the possibility of adding another section of the course. In some cases, the Registrar will approach you about the feasibility of doing this from the department's perspective. Perhaps a department member teaching an under-enrolled course can change their course roster, or perhaps the Dean would be willing to hire a visiting faculty member to teach that section. In other instances, it might be in the best interests of the students, department, and faculty to channel students into another course (perhaps a qualified visiting faculty member would be difficult to hire, and the course will be offered again in the following semester).
When seat spaces at the college are tight, try to avoid-during spring registration-overenrolling introductory courses and cutting into spaces otherwise reserved for first-year students. The Dean and the Registrar may be counting on a certain number of open seats for first-year students in planning for the upcoming academic year. Consider whether, instead, upper-level students can be nudged into upper-level courses for which they have pre-requisites. You may need to explain this to your department faculty.
The Dean monitors pre-enrollment, and any course with fewer than six students enrolled will raise a red flag and can be cancelled by the Dean. Such courses are always considered on a case-by-case basis. If there is very low enrollment before Accommodation Evening, you might wish to advertise courses through email to advisors or through campus flyers. If the course will be taught by a visitor, you could share information about the instructor. If the course is still under-enrolled after Accommodation Evening, it might be best to cancel the course and have the faculty member do something else. It might be that they can offer a second section of a course that is heavily enrolled, or that some special project for the department or college can be assigned. Any such scenario needs to be discussed with the Dean.
Is there a pattern of a faculty member often getting low enrollments? If so, it is time to have a conversation; is there a way to re-conceptualize courses so that they will draw more students?
Is there a pattern of many courses in the department, taught by more than one faculty member, getting low enrollments? See the section on "The Department Curriculum" for some questions that could guide a wider departmental conversation.