  We theoretically investigate non-Hermitian $p$-wave Fermi superfluidity in
one-dimensional spin-polarized Fermi gases which is relevant to recent
ultracold atomic experiments. Considering an imaginary atom-dimer coupling
responsible for the three-body recombination process in the Lindblad formalism,
we discuss the stability of the superfluid state against the atomic loss
effect. Within the two-channel non-Hermitian BCS-Leggett theory, the atomic
loss is characterized by the product of the imaginary atom-dimer coupling and
the $p$-wave effective range. Our results indicate that for a given imaginary
atom-dimer coupling, a smaller magnitude of the effective ranges of $p$-wave
interaction is crucial for reaching the non-Hermitian $p$-wave Fermi superfluid
state.
