Let's assume an aircraft for hire's 100-hour inspection is about 20 hrs past due (120 hrs since the last 100-hour inspection). Can I just say that the aircraft is not airworthy and the aircraft cannot be operated? Or, if I'm the owner, can I operate it just for personal flights? Is this illegal?
FAR 91.409(b) says:
Except as provided in paragraph (c) of this section, no person may operate an aircraft carrying any person (other than a crewmember) for hire, and no person may give flight instruction for hire in an aircraft which that person provides, unless within the preceding 100 hours of time in service the aircraft has received an annual or 100-hour inspection and been approved for return to service ...
According to a literal reading of the regulation, it only applies to operation "for hire" and not to the owner(s) flying it for personal use. So, in theory, what you propose is legal.
However, if an FAA inspector ever reviews the log books and sees that you went over 100 hours between successive 100-hour inspections, you would need to provide evidence that every such flight was not for hire, which could cost you significant time and effort.
So, while it is technically legal, in practice it is unwise. If the plane is regularly used for hire, get it inspected every 100 hours regardless of the nature of specific flights.