Der Fall: The case. Fall(s): In case of.
Das Mittel: The means. Mittels: By means of.
As an English speaker, I think of an s as a "pluralizer." But in these instances, the meaning of the noun-s sequence seems to be a construction of "preposition noun of."
What are these cases an example of? To take off on a comment below, what does it mean that s is a "genitizer?"
And are there many more such applications?