Saruman and the Nazgul
 

In Chapter ten of book four; 'The Palantir' in the two towers, Pippin looks into the palantir and a Nazgul flies over their campsite on it's way to Isengard to see what Saruman is supposedly 'up to' right after the 'Voice of Saruman' and the breaking of his staff.

Gandalf states "He has power still, I think, while in Orthanc to resist the Nazgul. He may try to trap it, or to kill it's steed." Something along those lines anyway.

That's all the detail the book goes to on that matter, so any ideas as to what could have happened?

I think that this Nazgul didn't come to mess with Saruman yet. He was just supposed to find out what's going on, and then get instructions and/or help to act. This Nazgul flew back over Edoras, didn't he? He could have went off to report to Sauron or something.

Like Galadriel said, I don't think the Nazgul Gandalf and Pippin see was sent to deal with Saruman, just sent to get information. Sauron had not trusted Saruman and wanted to find out what he was up to. When he saw a "hobbit" in the Palantir, he assumed this Hobbit was Saruman's captive in Isengard and Saruman may have also taken the Ring. However, remember Aragorn (I think the next day if I remember correctly?) challenges Sauron thru the Palantir. Sauron then pre-maturely starts his attack on Gondor because he thinks Aragorn (being Isildur's heir) now has the Ring and plans to use it against him.

As The Mouth tells everyone, Sauron would handle Saruman's treachery eventually, but right now the more pressing matter is getting the Ring, which he believes Aragorn has after Aragorn challenges him in the Palantir.

For what could have happened, I think Gandalf's words are still accurate. There's a part in Unfinished Tales (Hunt for the Ring) where the Witch-King makes his way to Isengard to get information, Saruman is able to deceive him and had the power to send the Wiki running away, tattling back to his boss what a meanie Saruman had been. At the time when Saruman's staff is broken, I don't think he would have had the power anymore to challenge the Witch-king, but a single Nazgul...yes.