Yes, I've seen them do this too. They're "reaching" for more light, out from under the shade of the mother plant.
You could cut them off when they do that if you don't like the way it looks. Just stick the cutting in some potting soil in the shade and keep it moist, and it will probably root, too. You might even be able to separate the flopping stems with some roots attached, which will give them a big boost on getting established as their own plant.
