Please give me some real and significant examples of where there can exist passive adversary/attacks but no active ones.

some guys have challenged me about the usefulness of a system that is safe against passive adversaries but is not so against active ones. it seems that they think, in practice anywhere eavesdropping is possible there will be the possibility of active attacks too.
they caused me to doubt regarding this myself because i couldn't find any good example to prove it (that protecting merely against passive attacks is worth enough to be implemented where protecting against active ones is not possible or is much more difficult).