Is there a name for prior distributions for which the actual value is in the support / has positive probability?

Question

I was wondering whether there is a name for prior distribution $P$ over some parameter $\theta$ for which the actual parameter $\theta^*$ is in the support of $P$ (or has positive probability for a discrete prior). I am aware that the whole idea of a prior is to assume that $\theta^*$ is in the support, but generally a prior could also be just "incorrect". So, I was wondering whether there is a name for these "proper"/"correct" priors.