Graduate school is very different from undergrad. As an undergraduate degree has become more and more necessary to live a middle-class lifestyle, many sources - including the federal government - have put in a lot of money and resources to try to make that achievable for more low-income students. So there are grants, scholarships, and low-cost loans for undergraduate students offered by both the federal government (and some state and local governments) and by private organizations, including the universities themselves.
Graduate school, however, is seen more as a choice a student can make to further their career - and the burden of paying for it is often seen as the student’s responsibility.
If your goal is a PhD, those programs are usually “fully funded” - i.e., your tuition, fees, and health insurance are covered by the department/university and you also receive a small living stipend (usually in the $20-35K range). You shouldn’t have to borrow money to cover the costs of attending a PhD program.
If your goal is professional school (like law, medicine, or business), those programs are usually financed primarily by loans. The return on investment in medicine and a few of those really highly-ranked law and business programs is high enough to make taking those loans worth it for many graduates.
If you are referring to any other academic or professional master’s program, the expectation there is also that students will finance these out of their own personal resources - which usually means that students have to take out significant loans to finance these degrees, too. Whether or not you should do that depends a lot on the program itself and how much money you expect to make in the future.
The Department of Education does match the cost of attendance: that’s why graduate PLUS loans exist in the first place. But Direct loans have special repayment provisions that are intended to help primarily undergrads, and because they cost money, they do have to be capped at a certain amount. (It’s also a protective mechanism; allowing borrowers to easily take on hundreds of thousands of dollars of unsecured debt is part of what fueled rising tuition rates and our current student debt crisis.) Do note, though, that the federal government’s bar for an “adverse credit history” may be a lot lower than yours, so I would still apply for a PLUS loan or at least call up the DoE to talk about your situation.
Sometimes, universities or departments have scholarships for certain students they want to woo to the school. There are also sometimes special federal programs or programs run by nonprofits to provide funding (like The Consortium for underrepresented students interested in an MBA, or HRSA nursing scholarships). I’d talk to the university/ies in question to see if they have opportunities like that - although usually, applying for grad school is the same application to get that finding.
This doesn’t mean that graduate school has to be a pipe dream, though; it may just mean that you have to delay it for a while while you get your credit in order.