We know if we can find CRLB and an unbiased estimator whose variance is CRLB, then this is UMVUE. But, what if CRLB is unattainable? Can we still find UMVUE?
Also, what if $f_x(x|p)$ does not satisfy the regularity conditions needed for the Cramer-Rao Inequality to apply? How do we find UMVUE?