If the magnitude of the values is very small, there isn't really anything to worry about. It is a result of the finite complex infinitesimal added to the denominator of the Hamiltonian. In theory this should tend to zero, but we cannot do that numerically. You can in principle try to decrease it (greens_function_infinitesimal), but the risk is that the calculations become numerically unstable, so it's generally not worth the trouble; just ignore the negative values.
If the magnitude is large (say, above 1e-4) it could indicate that the calculation has converged to a non-physical state (for instance with zero electrons in the central region).
