people and animals can not detect movement, all they can detect a change in movement (direction or velocity), if you think about being in a car, you don't feel like you are moving at a steady speed on a motorway, but you can feel if the car brakes, accelerates or turns.
if the earth was to slow down gradually then nobody would notice the change in movement as it would be below the threshold that we can detect (we would notice the days getting longer fairly quickly though)
If the earth was to suddenly stop then we would most certainly be able to detect the change.