  We study an interacting one-dimensional gas of spin-1/2 fermions with
two-body losses. The dynamical phase diagram that characterises the approach to
the stationary state displays a wide quantum-Zeno region, identified by a
peculiar behaviour of the lowest eigenvalues of the associated non-Hermitian
Hamiltonian. We characterise the universal dynamics of this Zeno regime using
an approximation scheme based on a effective decoupling of charge and spin
degrees of freedom, where the latter effectively evolve in a non-Markovian way
according to a non-Hermitian Heisenberg Hamiltonian. We present detailed
results for the time evolution from initial states with one particle per site
with either incoherent and antiferromagnetic spin order, showing how the two
non-equilibrium evolutions build up drastically different charge correlations.
