Employees of Google that work on GoogleX projects that graduate no longer technically work for Google, but for the new company and they no longer receive Google shares, but new company shares (in this case Waymo, Loon is another example [0]).
This forces the company and employee incentives to be aligned since the value of the employee equity is tied to the success of the specific GoogleX project and not Google itself.
When a company graduates if a lot of employees don't want to stay on the project and choose to stay at Google, that itself might be a bad sign (though it could also just be employee risk preference).
I think companies graduate when they're less pure R&D and closer to marketability. If they can't survive on their own at that point it may be because there isn't a market, the timing isn't right, or any other reason that can cause a startup to fail.
This system prevents Google from pouring money into something that's never tested in an environment where it can actually fail. It puts moonshot projects in an environment where they're truly tested and don't just become places where money is spent without any ability to measure success.
It's my understanding that graduated companies have their own hiring methods and can make their own independent decisions in general. They would also need to raise their own money.
[0]: https://loon.com/