Is there any processes involving weak interaction that preserve the strangeness for $S \neq 0$?
I can't find an answer to it on net or anywhere else, generally it is true that weak interaction changes strangeness by 1 unit.
Answer
Sure, your PDG reminds you of the strangeness-conserving decays of $$ \Sigma^\pm \to \Lambda e^\pm \nu , $$ where the antineutrino is meant to accompany the electron, mutatis mutandis.
That is, either uus or dds decays to uds , with a very small branching ratio, since, as you are implying, the heavier s is much more likely to decay to a light quark. But, in these highly informative/insightful cases, it is a light quark that weak transmutes to its isopartner.
So it is not true that weak interactions need change strangeness.
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