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I'm not a physicist by any means, but I would hypothesize that the slowest way would be to somehow get the object into a slowly decaying, nearly-geostationary orbit around Earth, closer than the Lagrange point between Earth and the Moon. Eventually its orbit will decay enough that it will just fall into our atmosphere somewhat "straight down", making it a matter of calculating the object's terminal velocity.
I'll probably be wrong about many things here, but it'll be interesting to learn when someone corrects me.
For anything that's captured in an Earth-centric orbit, it's never going to end up falling "straight down". Closed Earth orbits barely decay at all, except from atmospheric drag. For anything that started from a closed orbit, the last few years are almost always a circle or ellipse that barely brushes against the upper edges of the atmosphere.
For such orbits, drag is mostly applied near the lowest point on the orbit (perigee), and drag forces applied there will mostly reduce the height at the other end of the ellipse (apogee). Even if you start from a highly elliptical orbit, this means the decaying orbit becomes more and more circular. Eventually, all parts of the orbit are inside the atmosphere and the loss in altitude starts getting faster and faster, but the velocity is still mostly horizontal.
The good news is that the concept of specific orbital energy applies to any initial orbit. For objects coming from outside Earth's sphere of influence, terminal velocity remains a good lower bound.
Aren't you assuming a solar system object though? Forget probabilities and statistics; what about an interstellar object with ideal keyholes to cancel out velocities coming from any vector.
I can't get the picture out of my head of a plane stalling a few feet off the ground and coming to rest, or really the countless similar odd scenarios with a coin rolling around a large vortex toy/simulator that is used for grade school children to help illustrate physics and gravity. There are times when the coin loses all of its velocity and stops suddenly. Or better yet, if you've ever played golf and had a ball round the cup and get tossed back out right on the edge of the cup.
You can have any trope you'd like. Indestructible, natural ablatives, astroid made of Avi Loeb mystery meat stellar sail, ideal shapes, anything, heck detach pieces from a spinning planet killer moments before primary impact destroys everything.
No, there isn't anything like that. Big heavy objects fall. Falling objects are moving fast when they hit the ground. Further details are irrelevant.
Are you absolutely sure that you've seen a coin in those vortex demos just stop? Coins falling over doesn't count, there's nothing like that in space. Otherwise, they are moving at quite a clip when they reach the bottom of the funnel.
The one possible exception is when you detach part of the mass. If your vehicle removes some mass and launches it, you can use the reaction force to slow down. This is what a rocket engine does, for example. (Note the propellant will still impact at very high speed, as evident from the plume of any rocket landing.) The higher the relative velocity of the reaction mass, the less you'll need to come to a complete stop. But at this point we are talking about a manmade vehicle, not a naturally occurring rock.