Independent fonds would be a big one. Otherwise, independent researchers that finance their own research (In the case of the LK-99 research many lists had independent researchers names with Twitter links where they publish their research).

I am sure one can easily think up more ways to figure financing of (scientific) projects.

Where does the money in the funds originate from? Who set the original goal of the fun and the research direction?

when research is independent self funded, the direction is set by yourself.

When financing come from an independent fond, the board of that fond according to the purpose.

But where does the money in both cases come from?

Either you need to need to be indipendently wealthy or follow the desires of who or whatever gave the funds to the foundation.