Energy seems to quantum tunnel through normally impenetrable barriers, so I wonder why not the back side of an event horizon?
Actually, there is a phenomenon of quantum tunnelling and black holes. It's related to Hawking Radiation! Hawking Radiation can in fact be modelled as a qauntum tunnelling effect. Here are two papers discussing the quantum tunnelling from black holes: quantum tunnelling from three dimensional black holes and quantum tunnelling in black holes. Another paper discussing quantum tunnelling can be found here. Here is the paper where Hawking Radiation is modelled as a quantum tunnelling effect.