Some professors have “hard money” jobs where the university covers most/all of their salary; startup packages that are meant to help you get a grant are pretty common, as are fellowships or TAships for students.
However, I don’t think most universities cover much of the actual research expenses.
As for the patent, most places offer a split with the inventor, and may not patent everything; they have a right of first refusal though.
Some professors have “hard money” jobs where the university covers most/all of their salary; startup packages that are meant to help you get a grant are pretty common, as are fellowships or TAships for students.
However, I don’t think most universities cover much of the actual research expenses.
As for the patent, most places offer a split with the inventor, and may not patent everything; they have a right of first refusal though.