Upvote:5
Never seen it happen and really do not think it would be practical. It takes quite a lot of power to move a train and its inertia means that it takes a long time to stop.
One would not only have to stop the train and, depending on regulations, move it back to the platform to open the doors and allow boarding. The train would depart again later and everyone would be late just for one person, so it is not good for logistics. Might even delay an incoming train in stations where a platform is shared by multiple routes.
It is possible that there is a train somewhere that would stop for a late passengers but certainly expect this not to be the norm.