I can think of several relevant situations.
While it is not strictly part of the "case file", it isn't uncommon in commercial lawsuits between competitors (e.g. trademark disputes) for some documents that are disclosed in the case to a plaintiff to be disclosed on an "attorney's eyes only" basis pursuant to a protective order entered by the judge in the case.
Typically, this would involve documents that contain trade secrets that cannot be easily redacted from information that the plaintiff is entitled to learn about.
Conceivably, such documents could also be filed "under seal" in support of a motion.
In Camera Review
Sometimes, in the course of a case, a defendant will claim that certain documents are "privileged" from having to be disclosed, for example, because they including attorney-client confidential communications, and the plaintiff will dispute that fact. In those circumstances, sometimes the judge is shown the document itself which is not made available to the plaintiff, in order to allow the judge to make that determination, especially in a case headed to a jury trial. This process is called in camera review.
Temporary Lack Of Disclosure Of Ex Parte Motions For "Tactical" Reasons
I can image circumstances where something that is the basis of an ex parte motion (e.g. a request for permission to enter into a party's premises to search for documents or evidence or disputed property, without prior notice to prevent the things from being concealed or destroyed), would be granted "under seal" and not available to the plaintiff (and possibly not even listed in an official register of actions) until the ex parte motion which was granted is carried out. But, the non-disclosure to the other party in these circumstances usually wouldn't be a permanent matter.
It is much more common for this to happen in a case where the defendant is not allowed to see something filed by a plaintiff than the other way around.
Documents implicating national security can also sometimes be filed by the other party with the court "under seal", typically in support of a motion to have the plaintiff's case or part of the plaintiff's case dismissed on the grounds that this would risk a revelation of state secrets.
Sometimes, when the attorney, but not the client, has a security clearance, these documents can be made available to the attorney, but not to the client, on an "attorney's eyes only" basis.