  Large three-body losses in a three-component Fermi gas confined in an optical
lattice can prevent the occupation of a lattice site by three atoms. This
effective constraint not only gives rise to a suppression of actual three-body
loss, but stabilises BCS pairing phases by suppressing the formation of trions.
We study the effects of the constraint using bosonisation and density matrix
renormalisation group techniques (DMRG). We discuss the case of lithium
experiments, and study the dissipative dynamics including loss using
time-dependent DMRG with quantum trajectories methods.
