Well it's a matter of perspective. It is not possible to transmit information across an event horizon. So the position of the particle that has crossed the event horizon cannot be transmitted at all, so it has no position in space different from the black hole's own position. That's the quantummechanical view, very mathematical. It can only be expressed as X, so it must be X.
In relativity theory it is actually more complex than that. Think about what an outsider (like the particle that's about to become hawking radiation) sees when you fall into a black hole. Because space itself is falling into the black hole, it takes ever longer for light to cross the distance between you and the observer. So as you approach the event horizon, first, you appear to slow down. Now this slowdown will also produce a fading effect, and a redshift. The fading effect is what's important. Whatever process produces the light travelling from you to the observer will itself slow down, so the number of photons transmitted will decrease as you approach the event horizon. Then, at the crossing point, the time for any photon to reach the observer becomes infinite, which means the photon will never be received by the observer. So what happens to an electron is the same. As it approaches the event horizon, the magnetic field of the particle fades, and the field of the black hole itself strengthens at the same time. When the particle hits the event horizon, it's field is gone.
This is why one might refer to a black hole as a location where time ends.
You should not think of matter falling into a black hole as getting consumed. There is a difference of perspectives here. What's described above this line is what one sees if observing from a comfortable distance away from the black hole. For the person falling inside of the black hole, assuming the black hole is sufficiently large, nothing extraordinary would happen. The only real phenomenon you'd see is that the distance between you and any object (not just the ones outside of the black hole) would get larger by itself. Including the distance between you and the black hole itself.
An intriguing observation you can make is that if you look at galaxies' movements from earth, what do you see ? Well, the distances between all of them are getting bigger in all directions. Suppose you place dots on a balloon, then inflate it, the distance between all the dots increases. The same is happening in 3 dimensions to galaxies. And, guess what, the edge of the universe (as measured as being "just behind" the farthest object we can see, or alternatively where the redshift would turn infinite) is exactly where you'd expect to find an event horizon (we only have accuracy for that of half a billion light years, but still, pretty big coincidence). Do we exist inside a black hole ?
Since we have never seen negative mass particles, we don't actually know whether they exist or whether gravity attracts or repulses them. While it is true that electromagnetism can both attract and repulse, that is not a given for fundamental forces. The strong force only attracts, no matter the charges or any other property of the particles involved. Since we don't have a theory that has both gravity and the other forces we can't calculate this. Since we don't have any test material we can't simply test it out. Einstein's theories claim that gravity always attracts, even particles with negative masses. Now this theory doesn't have a good basis for that claim as it doesn't have negative mass particles, but historically it has been a mistake to bet against it.
We also don't know why there is an imbalance of "negative" mass virtual particles into the black hole. The reason black holes lose mass in this process is simply because of conservation laws. You'd expect 50-50 chances of losing mass but that doesn't happen in practice. Why ? No idea. Some explanations include that particles inside the black hole don't have to follow conservation laws, only the black hole itself and anything outside of it. This would mean that inside the black hole another hawking radiation particle came into existence, with positive mass and everything. Since this can never affect anything outside, this does not actually violate any laws of physics. It is a bit of a moot point though, like asking what happens to a number after it's been divided by zero. There is no answer, anything can happen.
In relativity theory it is actually more complex than that. Think about what an outsider (like the particle that's about to become hawking radiation) sees when you fall into a black hole. Because space itself is falling into the black hole, it takes ever longer for light to cross the distance between you and the observer. So as you approach the event horizon, first, you appear to slow down. Now this slowdown will also produce a fading effect, and a redshift. The fading effect is what's important. Whatever process produces the light travelling from you to the observer will itself slow down, so the number of photons transmitted will decrease as you approach the event horizon. Then, at the crossing point, the time for any photon to reach the observer becomes infinite, which means the photon will never be received by the observer. So what happens to an electron is the same. As it approaches the event horizon, the magnetic field of the particle fades, and the field of the black hole itself strengthens at the same time. When the particle hits the event horizon, it's field is gone.
This is why one might refer to a black hole as a location where time ends.
You should not think of matter falling into a black hole as getting consumed. There is a difference of perspectives here. What's described above this line is what one sees if observing from a comfortable distance away from the black hole. For the person falling inside of the black hole, assuming the black hole is sufficiently large, nothing extraordinary would happen. The only real phenomenon you'd see is that the distance between you and any object (not just the ones outside of the black hole) would get larger by itself. Including the distance between you and the black hole itself.
An intriguing observation you can make is that if you look at galaxies' movements from earth, what do you see ? Well, the distances between all of them are getting bigger in all directions. Suppose you place dots on a balloon, then inflate it, the distance between all the dots increases. The same is happening in 3 dimensions to galaxies. And, guess what, the edge of the universe (as measured as being "just behind" the farthest object we can see, or alternatively where the redshift would turn infinite) is exactly where you'd expect to find an event horizon (we only have accuracy for that of half a billion light years, but still, pretty big coincidence). Do we exist inside a black hole ?
Since we have never seen negative mass particles, we don't actually know whether they exist or whether gravity attracts or repulses them. While it is true that electromagnetism can both attract and repulse, that is not a given for fundamental forces. The strong force only attracts, no matter the charges or any other property of the particles involved. Since we don't have a theory that has both gravity and the other forces we can't calculate this. Since we don't have any test material we can't simply test it out. Einstein's theories claim that gravity always attracts, even particles with negative masses. Now this theory doesn't have a good basis for that claim as it doesn't have negative mass particles, but historically it has been a mistake to bet against it.
We also don't know why there is an imbalance of "negative" mass virtual particles into the black hole. The reason black holes lose mass in this process is simply because of conservation laws. You'd expect 50-50 chances of losing mass but that doesn't happen in practice. Why ? No idea. Some explanations include that particles inside the black hole don't have to follow conservation laws, only the black hole itself and anything outside of it. This would mean that inside the black hole another hawking radiation particle came into existence, with positive mass and everything. Since this can never affect anything outside, this does not actually violate any laws of physics. It is a bit of a moot point though, like asking what happens to a number after it's been divided by zero. There is no answer, anything can happen.