Older garage doors might not have the same safety features that you can find in a newer door. These features include an electric eye, standard since 1993, which raises the garage door should anything cross in front of it.
Another safety feature is an obstruction detector which doesn’t allow the door to close on top of objects. To test if your garage door has this, place a roll of paper towels in the path of the door. When the door hits the towels, it should reverse.