  We introduce a system based on dual-core nonlinear waveguides with the
balanced gain and loss acting separately in the cores. The system features a
"supersymmetry" when the gain and loss are equal to the inter-core coupling.
This system admits a variety of exact solutions (we focus on solitons), which
are subject to a specific subexponential instability. We demonstrate that the
application of a "management", in the form of periodic simultaneous switch of
the sign of the gain, loss, and inter-coupling, effectively stabilizes
solitons, without destroying the supersymmetry. The management turns the
solitons into attractors, for which an attraction basin is identified. The
initial amplitude asymmetry and phase mismatch between the components
transforms the solitons into quasi-stable breathers.
