Before revision:  Even if the given system is perturbed so that the nonisolated solution disappears, the iteration still locally converges to a stationary point that approximates a  solution of the underlying system with an error bound in the same order of the data accuracy.
After revision:  Even if the given system is perturbed so that the nonisolated solution disappears, the iteration still locally converges to a stationary point that approximates a singular solution of the underlying system with an error bound in the same order of the data accuracy.