What happens if too many kids accept admission. Yes, I know the stats usually prevent this from happening. For example…Penn State accepts 25,000 students a year. Of that 9,000 attend. But, what would happen if say 15,000 decide to attend? Their is no way the school could handle that kind of influx. Has this ever happened anywhere?
Forced triples. Lots and lots of forced triples. 
Seriously, housing is the biggest issue when yield is higher than expected. They track yield carefully from year to year, and usually have a pretty good idea what to expect. The waitlist is a tool they use, too. A lot of schools accept a number where they expect their yield to come in slightly lower than the total they really want, and then they can go to the waitlist to fill up the class.
And pity the applicants the following year as the school needs to admit less freshmen
@intparent and @T26E4 are correct. In addition to forced triples, sometimes common spaces are temporarily converted for beds.
sometimes students are asked to defer starting college for a year.
I’ve heard of H do this when too many students said “yes”
^Usually you hear about the deferrals for students who otherwise wouldn’t get in (aka z listing)
If the school guarantees housing for frosh, that may mean higher density (e.g. doubles converted to triples) or less availability for upper class students if upper class students are not guaranteed housing.
There may also be more issues with space in classes if the school is not one of the super-wealthy ones that can afford to maintain plenty of reserve capacity in every class/department. http://talk.collegeconfidential.com/parents-forum/1556885-no-calc-101-for-you-p1.html describes what may have been an overenrollment situation in calculus 1 at an unnamed liberal arts college.
Yes, sometimes non-freshman are out put on a housing waitlist to leave enough housing open for a large freshman class if necessary (just in case yield is higher than expected). Once the college is confident that they aren’t over their planned number of frosh, they take older students off the housing waitlist. That happened to one of my kids her sophomore year. She did get housing, but only after the freshman class had room placements.
I feel like the deferrals are usually offered at initial acceptance, so that isn’t so much a yield management tool. At most colleges it seems to be for one semester. That allows them to keep their housing full – more older students study abroad in the spring, freeing up some housing, and this fills those spaces. And a few students leave by or at winter break, too.
Some schools also tend to defer students to the spring semester if need be.
Harvard has been suggesting that students defer a year in their acceptance letters for years. It has nothing to do with getting too many acceptances. They think it’s good for students educationally to take a gap year. Harvard also has a “z list” which appears to be mostly used as a way to placate wealthy legacies: http://www.thecrimson.com/article/2014/4/3/the-legend-of-the-z-list/
We visited some colleges with forced triples and one in early September where one of the common rooms was being used a dorm room - they said that the common rooms usually clear out within a few weeks as students drop out or don’t actually show up.
One of our tour guides was living in a triple by choice because he liked the reduced room and board costs.
Colleges figure out a way to make it work one way or another.
Sometimes colleges rent out blocks of rooms in hotels or apartment buildings.
My school had that happen one year and they were putting kids up in a hotel and bussing them back and forth.
Schools do handle it. A few years ago, U of Rochester had 9% more students accept compared to expectations. I know of another school that rented a hotel for the fall semester until enough rooms opened up.
Actually, now that I think about it. A few years back. A college near me housed students in a hotel right on the beach.
Admissions are based on a lot of statistics. Some schools assume more will accept than the statistics show and make few offers, knowing they can go to their waitlist if not enough accept and they need more to fill their class. For the other outcome, forced triples or alternative housing are common. I saw somewhere a statistic about how many freshmen drop out after the first quarter or semester and it was surprisingly high (depending on the school), so those forced triples go to doubles by end of the first semester.
That happened this spring at Stanford, when the class of 2019 yield was unusually high (higher, actually, than Harvard’s—perhaps in part because quite a few Harvard admits chose Stanford). There are some corporate apartments near campus that have sometimes been used to house students, and though there weren’t originally plans to do that this year, that’s what ended up happening (not for freshmen, though). A dorm that was previously a three-class dorm was also opened up to freshmen.
Seems like some colleges consistently have forced triples, year in and year out. To me, that is not an over enrollment blip, but an administrative decision that they don’t mind a little “over enrollment”. Extra revenue with little additional outlay of $.