Consider a car with wheels having a circumference of $\unit{1}{m}$, so if the wheel turns around once per second, the car has a speed of one meter per second ($\unit1{m/s}$) or $\unit{3.6}{km/h}$.
The car has a somewhat peculiar stop watch on the dashboard. I thas a single hand. The face is divided into 60 like sized parts suggesting that one round of the hand is 60 seconds or one minute. Yet it is mechnically connected to one of the wheels in the strange way such that the hand goes around once exactly for $60$ turns of the wheel.
If the car runs at $\unit1{m/s}$ it will make $60$ turns in one minute and the hand of the stop watch in the car will turn around once suggesting one minute has passed, all just fine.
Yet, obviously, if the car goes slower, the stop watch will show a "time" which is not the same time we would check on our wrist watch. In special and general relativity, the stop watch time is called the local time in the car.
In particular when computing the speed of the car based on the local time, we will find that the stop watch turns once, $1$ minute, for $60$ turns of wheel and the speed of the car is $\unit{60}{m}/ \unit{60}{s}$ = $\unit1{m/s}$, independent of how fast the car is going according to measuring the speed with our wrist watch.
Consider the car heading towards a curtain while being set up get slower and slower such that it comes to a halt exactly at the curtain.
If the car would be an "observer" and the curtain would be the event horizon of a black whole, you'll find descriptions a bit like: 1⇗
As the car approaches the curtain, according to its local time, its speed is still the full $\unit{1}{m/s}$, unchanged and in the limit as it approaches the curtain. Further, an observer in the car would not find this weird. Assume their metabolism is also strongly coupled to and synchronized with the wheel's turning: if she normally breathes 15 time per minutes, now its 15 times per 60 wheel revolutions. If she normally has a hard beat of 70 per minutes, it is now 70 per 60 wheel turns. And similarly down to the chemical reactions that make a living organism. For this observer the car will continue to move through the curtain, move on as if nothing specifically happened, and will eventually crash into a singularity of all cars that already crashed into it before.
Sounds weird? I think so.
Though John Rennie says on Physics Stackexchange quite clearly: "in the coordinate system of an external observer the infalling object never crosses the event horizon", that is, simply put, for all practical purposes the car does not run through the curtain, ever. Which sounds relieving. :-)
But it leaves a conundrum about all those black holes recently detected, crashing into each other, and the singularity inside the event horizon:
According to my calender and clock, when did, in the last 16 billion years (which is a lot less then infinite billion years), stuff pass through any event horizon at zero speed to join any singularity behind? Do we have singularities behind event horizons anywhere, right now, in this universe or do we rather have to wait an infinite time first?