I wouldn't say they stop moving. But they can slow down the last few weeks. It gets tight in there! Lol. You may feel more gradual movements like arms stretching as opposed to karate kicks like you did before. You should still be able to do kick counts and count movements though :)

Everyone's body is different and everyone's baby is as well

My baby moved the whole time, she moved during contractions, the whole way to the hospital.

She might stay active but it all depends on the baby