The difference between (11a) and (11c) suggests that pied-piping of prepositions is obligatory in sluicing.
In German, pied-piping in sluiced clauses is pretty much obligatory, unlike (most cases in) English (cf.
Focusing on cyclic movement and certain questions connected to it, he investigates the extent to which successive-cyclic movement, partial movement,
pied-piping, secondary movement under
pied-piping, his own 2003 stranding generalization are amenable to a unifying treatment, and if so what role the notion of a phase might play in such a treatment.
Additionally, whose-phrases constitute a case of
pied-piping. See (6)-(7) below.
Of the two mechanisms generally available in Present-Day English relative clauses whenever a prepositional object is relativised, preposition-stranding is the only possibility in Old English infinitival relatives,
pied-piping not being available until the fourteenth century.
He identifies features of
pied-piping that hold true across different languages, proposes how to account for them, and contends that counter-observations can often be ascribed to independent reasons.