The same thing would happen as happens to you when you are a passenger in vehicle that makes a left or right turn at any speed / velocity. Your body was going in one direction at certain velocity and the person driving the vehicle probably decelerated some before starting the turn , Your upper body wants to keep going in the direction was going in while your hips go in the same direction as the rest of the vehicle so your upper body sways to the side in the direction opposite to the to the direction of the turn because all parts of your body has mass and inertia..
This is WHY even if we ever are able to create warp drive engine or faster than light drive, we also have to develop inertial compensators as well, Because any time a space craft transition from faster than light speeds to sub-light speeds any human being would sill have the inertia and momentum and speed and get smashed into protoplasmic goo and broken bones..
When i figured out how a force a vector has BOTH direction and and magnitude, HOW the ENTIRE universe works was like an almost blinding flash of understanding. I really was being driven to physics class when that happened. For me it really was an Epiphany. i still made Cs in math and physics courses, but i understood how the ENTIRE universe worked at macroscopic scales of size. 40 years later i am STILL trying to figure out how the minds of people work. ny father wanted to get across the trolley tracks before the street car could crash into the station wagon he was driving..
They will NOT stay put OR fall to the lowest point because they have mass, inertia AND momentum.