  We introduce a discrete linear lossy system with an embedded "hot spot" (HS),
i.e., a site carrying linear gain and complex cubic nonlinearity. The system
can be used to model an array of optical or plasmonic waveguides, where
selective excitation of particular cores is possible. Localized modes pinned to
the HS are constructed in an implicit analytical form, and their stability is
investigated numerically. Stability regions for the modes are obtained in the
parameter space of the linear gain and cubic gain/loss. An essential result is
that the interaction of the unsaturated cubic gain and self-defocusing
nonlinearity can produce stable modes, although they may be destabilized by
finite amplitude perturbations. On the other hand, the interplay of the cubic
loss and self-defocusing gives rise to a bistability.
