If you have already done the re-sit and you are now just waiting for the results, there is no provision to extend your Student visa.
If you have not done your re-sit yet, you can be sponsored for an extension to the re-sit date + 4 months. This is so even if you already have enough time on your visa to do the re-sit. This is normal and has always been so. However, your university can decide not to do that if they wish. But if the consequences are that you and, as you say, whole tranches of students are excluded from the Graduate route, that seems to be heavy collateral damage both to students and to the university in terms of their reputation and for PR purposes. It is worth pointing this out to the university and asking them to reconsider. Maybe you can get together with other affected students and query it, perhaps with support from the Students Union.
If they won't sponsor an extension, you will need to look into other routes, for example Skilled worker visa. You can be apply under the "new entrant" provision up to 2 years after completing your course, or until your 26th birthday.
UKCISA has a good and readable guide to the Skilled worker visa and other alternatives to the Graduate route.
https://www.ukcisa.org.uk/Information-- ... er-studiesI do not give immigration advice. I refer you to Immigration Rules, guidance, other online content and to your sponsor.
