  We study the impact of non-Hermiticity on the molecule formation in a
two-component spin-orbit-coupled Fermi gas near a wide Feshbach resonance.
Under an experimentally feasible configuration where the two-photon Raman
process is dissipative, the Raman-induced synthetic spin-orbit coupling
acquires a complex strength. Remarkably, dissipation of the system facilitates
the formation and binding of molecules, which, despite their dissipative nature
and finite lifetime, exist over a wider parameter regime than in the
corresponding Hermitian system. These dissipation-facilitated molecules can be
probed by the inverse radio-frequency (rf) spectroscopy, provided the Raman
lasers are blue detuned to the excited state. The effects of dissipation
manifest in the rf spectra as shifted peaks with broadened widths, which serve
as a clear experimental signature. Our results, readily observable in current
cold-atom experiments, shed light on the fascinating interplay of
non-Hermiticity and interaction in few- and many-body open quantum systems.
