scalar plpgsql functions and their stability flags

Good day experts...

Question on scalar plpgsql functions stability flags (immutable, stable)
regarding how it works in sql queries.

It is clear that for immutable/stable functions with constant parameters,
query planner could/should calculate value in a parse time and use it
directly in query, or at least once per query.

But it is unclear for me what exactly should/can happens when parameters
are bounded not to constant values but to query fields.
In such a case there could be some caching mechanics involved for
parameters combinations and result values.
Like building a hash table for that or something similar.

Can someone give me guidance on this matter.
What limits the usefulness of such a mechanism, if it exists.

Thank you.