I personally was referring to need-based grants, as part of financial aid applications. I'm not too familiar with fin aid in general, but thought these were a part (albeit small) of financial aid packages.
Need based grants can absolutely be expected depending on your school and your finances. If you/your parents don't make much, you will have high need. Some schools give loans for all your need. Other schools break it up between loans/grants based on their own formulas. If your parents make a lot, you won't get any aid, and will have to take out all loans. The worst debt comes when students have rich parents who don't help them out.
For example, no particular school or person, just an illustration:
Cost of attendance = $60,000
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Family contribution = $15,000 (translates to Grad PLUS loans if parents don't help)
School loan package = $25,000 (Staffords/Perkins/Sub/Unsub)
Grant = $20,000
Thus you would take $40k in loans yearly, for a total of $160k. Much better than total cost of attendance which would be $240k.
This situation only exists if a school has money to give. Schools like Cornell and Sinai told me grants exists. While USC sent me their finaid package and confirmed that they didn't have grants.