Just about every college that gives need-based financial aid expects students to contribute something (in terms of summer or part-time-in-the-school-year work earnings and/or a federal direct loan; sometimes, frugal living can cut costs and reduce the need for work earnings or loans). So the maximum need-based financial aid package for the lowest income and wealth student will give a net price of whatever the college’s expected student contribution is (which does vary between colleges, including different UC campuses).
Full rides without a student contribution generally involve merit scholarships. In a situation where a student gets both need-based aid and merit scholarships, colleges vary on how they apply. A common method is to apply the merit scholarship first against the expected student contribution (i.e. replacing loans and work study) and unmet need, before reducing need-based financial aid grants.