Do you remember how in schools you were taught atoms are the building blocks of matter? Later we come to know they are composed of subatomic particles, and then we find out protons and neutrons can be further broken down to quarks and gluons? If you are curious like me, you also realized later that these fundamental particles could be interpreted as excitations of their underlying quantum fields. We were also taught Newton's law of gravitation is "the" theory of gravity until we come across Einstein's theory of relativity. These are examples of how we are taught science inaccurately yet adequately for the time being. Similarly, this great article by Ethan Siegel talks about how Stephen Hawking explained his theory of "Hawking Radiation" using an analogy that is "a sufficient" explanation, but it's not "the" explanation.
This is the traditional explanation: Space is not empty, but there are particle-antiparticle pairs popping in and out of existence everywhere all the time. They are called "virtual particles." When one such pair pops in at the event horizon of a black hole such that one of the particles is "inside" the event horizon and the other one is "outside", the one on the inside gets sucked in whereas the other escapes. Hawking radiation is a consequence of these escaped particles. You can think of the particles being sucked in as "negative energy" particles. Energy is equivalent to mass; therefore, absorbing negative mass would result in the black hole losing mass or decaying.
It turns out, this is another case of inaccurate yet adequate explanations. Here is a more accurate picture of what's going on: Gravity is the curvature of spacetime, and extremely dense objects such as black holes have large amounts of spacetime curvatures around them. (This is actually why light "bends" when traveling close to the event horizon of a black hole. They are actually traveling in straight lines, but it is the spacetime that is curved, and they're not aware of it!). The objects we see around us every day can have zero motion energy when they remain still. Quantum fields, however, can never have zero energy (due to the infamous Heisenberg's uncertainty principle), and that's why empty space always has non-zero energy regardless of where you are. This is called "zero-point energy" or, at times, "energy of empty space." The value of the non-zero zero-point energy can vary depending on how large the curvature is. You can think of this as the strength of gravity at a certain place in spacetime affecting its zero-point energy. Whereas, if you go very far away from the black hole, there would be almost zero curvature of spacetime since there are no massive objects to cause it.
This difference in the zero-point energy due to the difference in the curvature of spacetime causes the emission of Hawking radiation. This implies the radiation does not come from the event horizon of the black holes, but from the curved spacetime around them. Since the black holes are causing the curvatures in the first place, they gradually lose mass over time. This explanation drastically differs from the traditional explanation of "negative energy" falling into black holes. Yes, this explanation implies other collapsed objects such as neutron stars also emit Hawking radiation. We have associated Hawking radiation with black holes and event horizons for so long that it's difficult for us to get used to Hawking radiation coming from other collapsed objects such as neutron stars.