Polarization-preserving fibers maintain the two polarization states of an orthogonal basis. Quantum communication, however, requires sending at least two nonorthogonal states and these cannot both be preserved. We present an alternative scheme that allows for using polarization encoding in a fiber not only in the discrete, but also in the continuous-variable regime. For the example of a helically twisted photonic crystal fiber, we experimentally demonstrate that using appropriate nonorthogonal modes, the polarization-preserving fiber does not fully scramble these modes over the full Poincar\'e sphere, but that the output polarization will stay on a great circle; that is, within a one-dimensional protected subspace, which can be parametrized by a single variable. This allows for more efficient measurements of quantum excitations in nonorthogonal modes.