Events inside a black hole occur for observers at those events.
But those events cannot be assigned a physically meaningful time coordinate – or “a when”, as put by Dr. Gabriel ‘Gabe’ Perez-Giz, (NYU/Princeton), in the video linked below – by an observer outside the black hole, so they do not occur for them.
In fact, he says, a black hole “is the set of all events that do not occur” for an observer outside that black hole. Which makes sense to me. After all, we consider the outer boundary of a black hole an event horizon.
Consider, for example, the Schwarzschild metric in Schwarzschild coordinates, which also describes a Schwarzschild black hole: a black hole whose electric charge is $Q = 0$ (“uncharged”, “electrically neutral”) and whose total angular momentum is $J = 0$ (“non-rotating”). It can be written (using sign convention $(+, -, -, -)$)
$${\mathrm ds}^2 = \left(1 - \frac{\mathrm r_\text S}{r}\right) {\mathrm c}^2{\mathrm dt}^2 - {\left(1 - \frac{\mathrm r_\text S}{r}\right)}^{-1} \, {\mathrm dr}^2 - r^2 \left[{\mathrm d\theta}^2 + \sin^2(\theta) \, {\mathrm d\varphi}^2\right],$$
where
$$\mathrm r_\text S = \frac{2 \, \mathrm G \, \mathrm M}{{\mathrm c}^2}$$
is the Schwarzschild radius; for a Schwarzschild black hole, the radius of its outer event horizon or simply its radius. ($\mathrm M$ is the black hole’s “mass”; see the video below for details.)
If you consider events with $r < \mathrm r_\text S$, i.e. inside that black hole, you can see that
$$\frac{\mathrm r_\text S}{r} > 1 \implies 1 - \frac{\mathrm r_\text S}{r} < 0,$$
which means
$$\left(1 - \frac{\mathrm r_\text S}{r}\right) {\mathrm c}^2{\mathrm dt}^2 < 0$$ and $$-{\left(1 - \frac{\mathrm r_\text S}{r}\right)}^{-1} \, {\mathrm dr}^2 > 0.$$
But the signs in the metric have a physical meaning: Previously we had chosen the sign convention such that the spacetime interval ${\mathrm ds}^2$ between timelike-separated events (that can be connected by motion with a relative speed less than $\mathrm c$) would be positive, and between spacelike-separated events (that cannot) it would be negative.
Now, inside the black hole, events that would be timelike-separated are (according to our convention) spacelike-separated, and vice-versa. So we cannot reasonably say that proper time elapses on a path connecting the former events. Therefore, we cannot assign a physically meaningful time coordinate to them, which is to say that for an observer outside that black hole – us, who are aware that there is a black hole –, they do not occur.
[There are other coordinates in which the Schwarzschild metric can be written, for example Gullstrand–Painlevé and Kruskal–Szekeres coordinates. But ISTM that the temporal coordinate there does not have a physical meaning; it is just a mathematical trick to avoid the coordinate singularity that appears in Schwarzschild coordinates at $r = \mathrm r_\text S$.]
Furthermore, I think that, if we use the fact that light from events inside the black hole cannot reach an observer outside as a guide, even events inside a Schwarzschild black hole do not occur for observers inside such a black hole who are at reception events whose angular coordinates ($\theta$ and $\varphi$) are not exactly equal to that of the emission event, as light from those events has to fall radially inward. This might be different for a Kerr or Kerr–Newman ("rotating") black hole.
(CMIIW)
See also:
And, I have to point out that, given its title, you could have found the first video at the time of posting already by a Web search, by simply entering your question there.
No, it "speeds up" instead. (More proper time elapses there than for you.)
"When you see someone from outside approaching a black hole, you see how they freeze in time as they get closer and closer to the event horizon [...]"
You have and repeat a lot of misconceptions that laypeople have about black holes. It is so much that even my few main short corrections are too long for this comment box. So I am referring you to a clarifying video by an astrophysicist instead:
https://www.youtube.com/watch?v=vNaEBbFbvcY
– PointedEars Jan 05 '24 at 14:26