If you're thinking about the liability waiver found in many licenses and contracts and EULA and other, they are often void, depends on the jurisdiction.
The official answer from Github that they take all input on purpose doesn't play in their favor.
I'm speaking specifically about the indemnity agreement that you get as part of a purchased license. It is the opposite of the liability waiver -- it is saying that the software publisher will take on responsibility in certain cases and with certain limits.
For example, if I purchase certain corporate Linux licenses, i'm protected against being sued if something in the distribution ends up having misappropriated code.
Having an indemnity clause doesn't mean that a company will automatically defend you or cover your expenses. You may have to sue them to enforce the contract and agree on the costs.
The answer to what will happen when companies are bitten, is that there will be series of lawsuits involving various parties (including GitHub), dragging on for a while and costing a fortune. The court will decide everything in the end (who's responsible for what, who cover the fees, who own the IP, etc...).
The SCO case was rather frivolous, I don't think there is much to take from it, except that if a US company is determined to sue and they have a billion dollar to go on forever, there's nothing stopping them to and it's a lot of troubles.
Which is relevant I suppose. It's only a matter of time until there's a major case putting GitHub Copilot in the spotlight and an aggressive company with deep pocket (think Oracle and the likes). We will certainly be reading about it everywhere the day it starts.
The official answer from Github that they take all input on purpose doesn't play in their favor.