  We analyze an unusual class of bosonic dynamical instabilities that arise
from dissipative (or non-Hermitian) pairing interactions. We show that,
surprisingly, a completely stable dissipative pairing interaction can be
combined with simple hopping or beam-splitter interactions (also stable) to
generate instabilities. Further, we find that the dissipative steady state in
such a situation remains completely pure up until the instability threshold (in
clear distinction from standard parametric instabilities). These
pairing-induced instabilities also exhibit an extremely pronounced sensitivity
to wavefunction localization. This provides a simple yet powerful method for
selectively populating and entangling edge modes of photonic (or more general
bosonic) lattices having a topological bandstructure. The underlying
dissipative pairing interaction is experimentally resource-friendly, requiring
the addition of a single additional localized interaction to an existing
lattice, and is compatible with a number of existing platforms, including
superconducting circuits.
