Disclaimer, I am not a physicist. There are two kinds of singularities related to black holes. The first kind are coordinate singularities, for example at the

Disclaimer, I am not a physicist. There are two kinds of singularities related to black holes. The first kind are coordinate singularities, for example at the event horizon in the Schwarzschild metric. Those are mathematical artifacts of the chosen coordinates and we can get rid of them by using different coordinates for calculations. The second kind are the ones at the center, where, for example, the curvature blows up to infinity. For those we do not know how to get rid of them. Still very few physicist will consider them any more real than the first kind, they are most likely an artifact of relativity not accounting for quantum physics or something like that. When it comes to naked singularities, we are concerned with the second kind of singularity, those at the center. They are usually hidden behind the event horizon because - in case of a non-rotating uncharged black hole - the Schwarzschild radius is positive and nothing from inside the Schwarzschild radius, where the event horizon is located, can reach the outside. For rotating or charged black holes the event horizon can however disappear, I think the Schwarzschild radius or its equivalent becomes complex. No event horizon, nothing hiding the singularity, i.e. a naked singularity. So the uncharged non-rotating electron has a mass and I would guess also a singularity in the gravitational field but its Schwarzschild radius is positive hiding this singularity behind the event horizon. That is, if you wanted to get close enough to the electron to have a look at the gravitational singularity, you would first have to pass through the event horizon of the electron and then you could unfortunately no longer tell us what you saw. Also the "electron" would now be 70 kg, I guess.