  We consider QCD factorization between hard and soft subprocesses in inclusive
reactions where the momentum fraction x of one parton approaches unity as the
hard scale Q^2 -> \infty, such that Q^2(1-x) is fixed. In this "BB limit" the
entire (multi-parton) Fock state containing the high x parton is coherent with
the hard subprocess. The soft contribution is given by a forward multiparton
matrix element. The BB limit corresponds to a fixed (large or small) missing
mass and is thus closely connected to exclusive production. We analyze the
Drell-Yan process h + N -> \gamma^* + X in detail, explaining why the virtual
photon is longitudinally polarized for h = \pi and transversely polarized for h
= p. The BB limit may be relevant also for other phenomena observed at high x,
such as the large single spin asymmetries of p p -> \Lambda^\uparrow X and in p
p^\uparrow -> \pi X.
