Some projects require contributors to assign ownership of their contributions to some legal entity (e.g. a company).

In that case, those contributors no longer have any control. It's all up to whoever the legal owner is.

However, many projects merely invite contributors to license their contributions to the project under the same terms the project already was under.

The Linux kernel is an example of this. It was released by Linus Torvalds under the GPLv2, and contributors added their own changes under the GPLv2, without assigning ownership to Linus. Linus only has permission to use those changes under the terms of the GPLv2. They don't belong to him; he's only using them in the Linux kernel under license from their creators.

So, there is nobody who can "take Linux private", because doing so would require the assent of lots of contributors; many of whom would be unwilling to go along with such a scheme.