From personal experience I can say that there was such a thing in the early 1990s. I was accepted to and attended an "elite" university, but left after one semester. I was not offered financial aid, and student loans were such that I could not have borrowed enough under Stafford or any other normal loan program to pay my tuition. I wound up transferring to a less expensive in-state public university and experiencing the best of serendipity so it ended well.