I can't even think of what you mean by the latter thing. Pretty much every game I've played you just stay on the floor.
It's just momentum. Object in motion stays in motion.
Think of a skateboarding game or a skateboard in real life. If you skate off anything, you don't fall to the ground instantly.
Most games ignore momentum for humans and throw them down. Like in botw I found a cliff next to a house. Should be able to run off the cliff to land on the roof but the game throws link down instead, unless you press jump to turn off the clamp.
Some games always clamp.
Some clamp most of the time.
Some never clamp.
I feel like i know a game that does this, but I can't place it.
A game where you would start falling onto the stairs.
I definitely prefer being locked to the ground.
Yeah I'm having trouble finding an example with stairs. Maybe death stranding.
EDT: death stranding is the complete opposite. Throws you down comically fast.