  Partial quenching allows one to consider correlation functions and amplitudes
that do not arise in the corresponding unquenched theory. For example, physical
$s$-wave pion scattering can be decomposed into $I=0$ and $2$ amplitudes,
while, in a partially-quenched extension, the larger symmetry group implies
that there are more than two independent scattering amplitudes. It has been
proposed that the finite-volume quantization condition of L\"uscher holds for
the correlation functions associated with each of the two-particle amplitudes
that arise in partially-quenched theories. Using partially-quenched chiral
perturbation theory, we show that this proposal fails for those correlation
functions for which the corresponding one-loop amplitudes do not satisfy
$s$-wave unitarity. For partially-quenched amplitudes that, while being
unphysical, do satisfy one-loop $s$-wave unitarity, we argue that the proposal
is plausible. Implications for previous work are discussed.
