There are TV shows that show martial art masters paralyze a person by hitting them on certain points. Personally, I thought this was cool and did a little digging. I want to know, is there a style of martial arts that does this through pressure points, and not just through brute force? Thanks!
The short answer is: no.
The longer answer follows.
First, as Macaco Branco mentioned in the comments, please see my explanation (debunking) of pressure points here:
Now as for paralysis, that's a different subject. Paralysis is caused by the signals from the brain not reaching the muscles. The only way that happens is by damaging the nervous system somewhere along the way.
Some pressure points are located close to a nerve complex. Nerves are pretty much everywhere in the body, so your chances of hitting one are pretty good. But pressure point theory doesn't actually deal with nerves. If you're hitting a nerve while targeting a pressure point, it's by accident.
You can attack the nerves specifically. Nothing wrong with that. In fact, Leopard style kung-fu actually makes it a point (no pun intended) to attack the nerves.
But will attacking a nerve actually cause paralysis? No. It would be extremely rare and nothing you could rely on as a method of self-defense. Most of the times a nerve is damaged, it's only going affect sensation. Part of your body will feel numb, some time after the initial electric shock feeling and pain subsides. And it might take weeks to regain that sensation, as the nervous system intelligently routes signals around the damage.
But losing motor control of a limb (paralysis) is very rare. Attacking a nerve on a limb can cause numbness and pain for a while, during which time they can still move their limb, but it might feel awkward and painful to them. Then they might simply decide not to use that limb, which accomplishes your goal even if it's not actually paralysis.
Severing a nerve is really hard, too. For the most part, hitting a nerve means damaging it temporarily, not actually destroying it. And motor function still works even if it's damaged.
If you really wanted to paralyze someone, you would attack the spine. But the bones of the spine have evolved to that particular shape for a reason. It's actually quite difficult to strike the spine, break it, and damage the spinal cord itself. It's possible, but usually not with bare hands or feet alone. And if someone is able to move and avoid your attacks, that makes it even more unlikely that you're going to be able to cause paralysis that way. Once again, this is an unreliable method of self-defense.
So no, there's not much truth to the way this is portrayed in movies and on TV, such as the new "Cobra Kai" series. In Cobra Kai, you see Daniel temporarily paralyze the arm of someone using a crane's neck fist strike to attack the underside of the arm. It would merely make the arm feel a painful shock and then sustained pain and numbness. Your opponent would still be able to use their arm, but they wouldn't want to because everything would feel painful - like prickly, painful needles everywhere. And it would require a decent amount of force to attack those nerves in order to have this kind of effect. You don't get it with a light touch.
Like I said, this is a valid thing in martial arts, attacking nerves. Some martial arts may say it's a pressure point strike, but they're really just using the location of the pressure point as a way of describing where to hit. Most of the time, you actually don't need to hit a specific point, because the nerves go all along the underside and inside parts of the arms and legs. But there are places which maybe give you the biggest response. There's nothing mystical going on in that case. It's just where the nerves are most accessible (easiest to hit).
Hope that helps.