Attainability of Fisher Information Matrix

We talk about attainability of classical FIM, in the asymptotic limit, FIM can always be attained:https://en.wikipedia.org/wiki/Maximum_likelihood_estimation#Efficiency

And also refer to this paper:

The Cramér-Rao bound can be established only if the FIM is strictly positive (and thus invertible). In this case, it can always be saturated, asymptotically in ν, by the maximum likelihood estimator.