Stopping Unfair Collateral Consequences from Ending Student Success Act or the SUCCESS Act This bill amends title IV (Student Assistance) of the Higher Education Act of 1965 to modify federal student aid eligibility criteria. Specifically, the legislation repeals a provision that suspends a student's federal student aid eligibility for a one-year, two-year, or indefinite period following that student's first, second, or third drug offense. Additionally, it prohibits the Department of Education from including on any federal financial aid form (e.g., the Free Application for Federal Student Aid) a question about an applicant's prior drug offense convictions.