Fiber optical parametric oscillators (FOPOs) are compact optical sources of coherent and broadly tunable light compatible with operation in unconventional spectral bands. Highly nonlinear silica fibers have enabled the development of FOPOs in the telecommunication wavelength band, but the strong material absorption of silica glass at wavelengths >2 µm limits its applicability in the mid-infrared (MIR) spectral range. In this work, we overcome this issue and report a FOPO designed entirely out of soft glass fiber. For this purpose, we combine an As2Se3 single-mode fiber coupler, an As2Se3 parametric gain medium, and a low-loss ZBLAN delay fiber to build the first all-fiber laser cavity made of soft glass. Two proof-of-concept FOPOs are presented, one driven by pure parametric gain leading to wavelength-tunable Stokes emission within the range 2.088-2.139 µm, and the other driven by Raman-assisted parametric gain leading to Stokes emission within the range 2.023-2.048 µm. This demonstration is a promising first step toward the development of fully fiberized MIR light sources.