Protecting Students from Failing Institutions Act - Amends title IV (Student Assistance) of the Higher Education Act of 1965 to require the Secretary of Education to discharge a borrower's liability on a loan under the Federal Family Education Loan (FFEL) program if the student borrower, or the student on whose behalf a parent borrowed, is unable to complete the program in which such student is enrolled due to the closing of a campus or branch of the institution of higher education (IHE).

Prohibits a student's period of attendance at a campus or branch that closed and prevented the student from completing the student's course of study from: (1) being considered in calculating the student's period of eligibility for additional assistance under title IV, or (2) counting towards the student's duration limit for Federal Pell Grants.

Provides such liability discharge and eligibility protections to borrowers who withdraw from an IHE no more than 120 days before the closure of the campus or branch of the IHE at which they are enrolled if that closure would have prevented them from completing the program in which they were enrolled.

Allows a borrower who receives a Federal Pell Grant for an academic year for enrollment in a program at an IHE campus or branch that closes to use the remaining amount of the Federal Pell Grant for such academic year at another IHE even if the borrower is considered able to complete the program in which the borrower is enrolled.