Not always, I was specifically talking about a Kerr black hole, yes, however they can have two event horizons. If the rotation is fast enough, these can cancel each other out leaving a naked singularity that is completely in view. It’s also important to realize that ONLY in a Schwartzchild model is the singularity zero radius and infinite density. A Kerr black hole would have a ring that is close to zero thickness but not quite, and the density is not infinite. So the question still posed is: What happens when this specific type of black hole cannot evaporate (since it cannot pull in one particle of a two particle virtual pair anymore without gravity around it) and it cannot deteriorate as nothing can leave its surface. There would be no gravity at this black hole except exactly at its surface and below, hence any decay would remain exactly where it was before.