  We show that constraints imposed by strong Hilbert space fragmentation (HSF)
along with the presence of certain global symmetries can ensure the reality of
eigenspectra of non-Hermitian quantum systems; such a reality cannot be
guaranteed by global symmetries alone. We demonstrate this insight for two
interacting finite chains, namely the fermionic Nelson-Hatano and the
Su-Schrieffer-Heeger models, none of which has a $\mathcal{PT}$ symmetry. We
show analytically that strong HSF and real spectrum are both consequences of
the same dynamical constraints in the limit of large interaction, provided the
systems have sufficient global symmetries. We also show that a local equal-time
correlation function can detect the many-body exceptional point at a finite
critical interaction strength above which the eigenspectrum is real.
