  We study a driven, spin-orbit coupled fermionic system in a lattice at the
resonant regime where the drive frequency equals the Hubbard repulsion, for
which non-trivial constrained dynamics emerge at fast timescales. An effective
density-dependent tunneling model is derived, and examined in the sparse
filling regime in 1D. The system exhibits entropic self-localization, where
while even numbers of atoms propagate ballistically, odd numbers form localized
bound states induced by an effective attraction from a higher configurational
entropy. These phenomena occur in the strong coupling limit where interactions
only impose a constraint with no explicit Hamiltonian term. We show how the
constrained dynamics lead to quantum few-body scars and map to an Anderson
impurity model with an additional intriguing feature of non-reciprocal
scattering. Connections to many-body scars and localization are also discussed.
