If it's theoretically possible to create an unbiased model (even asymptotically), this is not true for variance. To understand this concept, it's necessary to introduce an important definition: the Fisher information. If we have a parameterized model and a data-generating process pdata, we can define the likelihood function by considering the following parameters:
This function allows measuring how well the model describes the original data generating process. The shape of the likelihood can vary substantially, from well-defined, peaked curves, to almost flat surfaces. Let's consider the following graph, showing two examples ...
