I would assume any "grounding" stone would counter-act the "falling" aspect. Tiger Eye, Petrified Wood, Onyx. Any stone that is black, brown or red will help one feel more rooted.
Aquamarine and Bloodstone are sometimes called "stones of courage". Bloodstone especially enhances both grounding and the ability to recognize (and therefore let go of) chaos.
Blue Quartz is said to remove fear and inhibitions. On the other hand, you would want to avoid Blue Agate, which has a very "airy" energy.
Carnelian protects against negative emotions
Hematite encourages mental/emotional stability, and helps to remove negative energy.
Moss Agate improves the ego and self-esteem by providing emotional balance and enhancing the positive aspects of one's personality.
Sunstone is said to eliminate fear and reduce stress. Tourmaline does this as well, in addition to providing protection.
