Many students apply to Ivy League schools. However, there is always the possibility that they will not be admitted, so they also apply to “safety schools”—schools where they are fairly certain of being admitted. The term “safety” refers to the safety of the students applying successfully to a school.
 
The “safety school” term has been cited in print since at least 1963, and “safety college” since 1967.
 
   
Wiktionary: safety school
Noun
safety school (plural safety schools)
1. (US, colloquial) The least-desired among colleges and universities one applies to for admission, chosen as a contingency in case one is rejected from all others.
 
(Oxford English Dictionary)
safety, n.
attrib. U.S. colloq. Designating a college or university to which an applicant feels confident of being accepted, and to which he or she may have recourse if applications to other, preferred, institutions are unsuccessful. Freq. in safety college, safety school.
1963   H. Black They shall not Pass v. 67   Don’t worry..if Joey doesn’t make the prestige college of his choice. There will always be a place for him in his safety school.
1967   Chron.-Telegram (Elyria, Ohio) 24 Mar. 8/1   Even if he does take precautions, however, a student today may find himself turned down by his ‘safety’ college.
       
24 March 1967, Chronicle-Telegram (Elyria, OH), “How to get into college: ‘Matchmakers’ can help rejected students” by Benjamin Fine, pg. 8, col. 1:
Even if he does take precautions, however, a student today may find himself turned down by his “safety” college.
 
23 April 1969, Rockford (IL) Morning Star, “‘Fat Letters’ Are Talk of Spring at High Schools” by Linda Mathews (LA Times-Wash. Post Service), pg. B20, col. 6:
They spend hours calculating whether they can hold off responding to their “safety” school until word from “First Choice U.” arrives.
 
Google Books
Photographs of My Father
By Paul Spike
New York, NY: Knopf; [distributed by Random House]
1973
Pg. 11:
I apply to five schools. All but one reject me. I am going to my “safety” school, an academy in Pennsylvania named The Keaton School.
   
Google Books
Uncommon Women and Others
By Wendy Wasserstein
New York, NY: Dramatists Play Service Inc.
1978
Pg. 17:
KATE. Not as much as Vassar. I applied there as a safety school.
 
3 July 1979, The Advocate (Stamford, CT), “Coleman looking forward to private practice” by Stephen Bell, pg. 13, col. 4:
Coleman also said that a student’s “safety” college—one which a student thinks he will be accepted at in case he is not accepted at a preferred school—should be one the student really wants to attend, not one he merely settles for.
 
Urban Dictionary
Safety School
A school which you apply to in order to make sure you at least go to SOME college, in case you get rejected from everywhere else.
-Dude, did you get into Stanford?
-No, but I got a full ride to my safety school, Berkeley.
by the S Tree March 19, 2009
   
Business Insider
The 10 best ‘safety schools’
PETER JACOBS
Jul. 13, 2015, 11:31 AM
When students apply to college, it’s usually a safe bet to check out some schools they have a good shot of getting accepted to.
 
So-called “safety schools” often get a bad reputation for accepting most of their applicants, but many of the colleges are also top academic institutions.