In the same way that a series volume title can be advertised yet not published, sometimes there are ads in trade magazines or in post-text ad pages of the books themselves.
The Ben Lightbody series was advertised in several 1910s-era Altemus books. It was never published and probably never written.
The Clover Girls series was advertised by A.L. Chatterton in 1910 in Publishers’ Weekly, a trade magazine for publishers, booksellers, and authors.
Another way a phantom series can be known in the collecting community is when a bibliography or magazine includes one as a practical joke. This is particularly true in April Fool’s issues of the series book magazines. The Mattson-Davis bibliography of boys’ series books extends the work of Harry K. Hudson. One of their additions is the fictitious Zoobilly Boys series.
Phantom series are less common than phantom titles. Sometimes they can be a cruel joke on beginning and completist collectors.