What does it mean to patent a company?

It means that in a patent application or authorization, there is only one person or unit for the first author, owner and applicant of the patent respectively. "A work" usually refers to the first author of a paper or research report, that is, the most important contributor. And "a unit patent" refers to the unit to which the patent belongs, that is, the institution, company or organization to which the patent owner or applicant belongs.