Would a device that could allow you to safely fall from extreme heights without any kind of way to slow your fall be physically possible?

Video games and cartoons are fiction. There is no way to insulate yourself from the great deceleration when you hit the ground. 

yes, you can safely fall from any height safely

But above some level the sudden stop at the bottom will kill you.

It is called terminating deceleration.

you can't stop instantly while falling, that would be like hitting a brick wall at 60 mph. But if you allow some time for the stop, that is possible.

terminal velocity, let's take it at 200 km/hr which is 55 m/s. Let's assume the max deceleration a healthy human can take for a brief period is 20g, about 200 m/s².

to slow down from 55 m/s with a de-acceleration of 200 m/s will take about 55/200 = 0.3 sec. Is that acceptable? Anything less than that is not possible without damage....

distance traveled in that 0.3 s is ½at² = 9 m, hardly instantaneous.

In a stable, belly to earth position, terminal velocity of the human body is about 200 km/h (about 120 mph). A stable, freefly, head down position has a terminal speed of around 240-290 km/h (around 150-180 mph).

It goes without saying that a fall has to end by slowing down the falling object, so unless you are talking about an eternal fall which never stops, no, you cannot stop the fall except by slowing the object down.  The safety side comes in from the rate of stoppage, not the actual act of stopping.  The force has to be distributed over enough time that it does not exceed the strength of the human body to avoid any damage to the body.

Presumably, there are some energy-absorbing systems which spread the impact force out over time somehow.  What would they be?  Who knows, they do not actually exist in our technologies.  They are pretend-systems, not real things.