I want a foo that doesn't bar, such as a baz.
Is baz referring to a foo that does bar, or a foo that does not bar?
Neither. It's just an construction that is both ambiguous and logically incomplete.
As it stands, your imagined or intended foo could be one that by habit or external setting does not bar at all, or one that we must assume has the potential to bar but so far seems not to have done so (although we might be unequipped to tell).
The entire statement indicates that barring is somehow assumed to be in the general nature of foos. 'Baz' is some relevant designation in this area, not specifically defined but evidently related to a capacity for barring.
Right now, given this text, we must assume that any given foo could bar at any moment: we just don't yet know enough about it.