Well, these may well be the most extreme regions in space-time and the maths are some of the most difficult to solve (and honestly way over my head). Plus we would have to be able to marry GR and QM to fully describe black holes.
The way I see it, the vacuum fluctuations can form many kinds of virtual pairs, and when that pair consists of photons, then there is no problem at all since they always move at c and hence can escape the gravitational well (but they will be red shifted due to the extreme gravity). So most of the Hawking radiation will always be EM radiation.
Mass-bearing particles will form with the same small/limited energy from the vacuum, and their momentum and thus initial speed will be small too. In a normal gravitational well they would almost immediately fall back towards the event horizon, due to the extreme gravitation (it requires thrust for any mass to change/leave orbit, and these are not even in orbit).
In the ergosphere of a rotating black hole, nothing can remain stationary relative to the rest of the universe because that would require faster than light movement. This means particles are forced to move, even when initially stationary, and hence they gain momentum, which in turn can lead to the particle escaping the gravitational potential.
Of course, that is when only taking into account gravitational effects. The extreme magnetic fields surrounding black holes will also accelerate charged particles, and will probably have a bigger effect than frame dragging.