From Cramer Rao lower bound in Cauchy distribution in Daniel's reply they mention that such a bound exist if $\frac{\partial \ln L}{\partial \theta}$ can be factored.
Is this true? If so what do they mean by factored? If not, is there a way to show that a pdf/pmf doesn't have an unbiased estimator that attains the Cramer-Rao lower bound?
Also in the video https://www.youtube.com/watch?v=igQIsYAlKlY They say that the bound will exist if an unbiased estimator exists. So I only need to show that such an unbiased estimator can exists for a pdf/pmf for the bound to then exist?