::Q: Whose house is too big? A: Fred's _{house is too big}. - Possessor as answer fragment
::Q: When did they arrive? A: _{They arrived} At noon. - Temporal adjunct prepositional phrase as answer fragment
::Q: Why will they resist our help? A: _{They will resist our help} Due to excessive pride. - Causal adjunct prepositional phrase as answer fragment

This sort of data could easily be expanded. An answer fragment is possible for any constituent