There is a link to a youtube video of a BBC explanation of this, it features amongst others Bernard Carr, now Professor at Queen Mary, but Hawking's student at the time he did this work. Most of it is quite sensible, well at least the bits where Bernard Carr is speaking. But the explanation on the voiceover is that a particle and an antiparticle are created outside the horizon, and the antiparticle has negative mass and falls into the black hole reducing its mass.

This is utter nonsense, as a number of commenters on youtube have pointed out, antiparticles have the opposite charge to their corresponding particles, but have positive mass. No particles have negative mass, at least none yet discovered. I got the link to Hawking's article from one of the comments.

They cannot have let Bernard Carr have sight of that before putting it out, nor Hawking himself.