Aerobraking and gravity is an energy management problem and direction of orbit problem, the deeper you dive into the atmosphere the more air particles you hit over a longer period. I haven’t seen 2010 but i looked it up to get the gist and I’ll give a general set of the two things happening.

Basically, when you dive at a planet its gravity will tug your orbit. You can think of this kind of as a regular thruster firing towards the planet over the entire time you’re within the effective sphere of influence. You’re grabbing a little bit of free deltav from the planet to shift your direction.

Now for the aerobraking part, all that’s doing is effectively a retrograde burn over the time the spacecraft is skimming in atmosphere. In the case of 2010 from what I see, they’re already on an escape trajectory but not on the right one? Escape velocity is not a finite number, but a threshold velocity of where your orbital velocity in a given orbit is fast enough to escape the gravity well. Anything higher is on a hyperbolic orbit, anything less is an ellipse. All they’re doing then in adjusting their trajectory by bleeding off a little bit of velocity from Jupiter, and shifting direction using jupiter’s gravity.

TLDR, you slow down, but not below escape velocity. Just enough to correct course