tig log foo will display only log entries for foo.
It would be nice if tig log foo would only display stashes changing foo.

I've not really investigated, but it might be as simple as passing through (some) options similar to how it is done for tig log.
But e.g. tig log -S "some pattern" (also with specifying HEAD explicitly) results in tig: No revisions match the given arguments. (i.e. it behaves different from git log … / does not handle the -S option already).
So it appears that for tig-log already handling of options could benefit from passing through / handling more?

Currently tig stash appears to ignore any options/arguments (apart from -h).