I had a pachyphytum at home that was dropping leaves just as aggressively! I panicked at first, then figured it out - it's a normal plant stress response and a sign of watering issues. When a succulent goes from drying out completely to getting too much water, its tissues become weak and the leaves don't stay attached properly. Check your soil: it should dry out completely between waterings! In winter I water my pachyphytum only about twice a month, just giving it minimal moisture.
Another important thing - it could be cold or drafts. If the shelf is near a window where air currents pass through, or the plant is in a cool spot, it starts shedding leaves as a defense mechanism. Move it to a warm place with good light but no drafts. Try not to touch it or move it around unnecessarily - every movement stresses it out when it's in this condition.
Don't worry about saving the leaves - the ones that fell can actually be propagated! Put them on dried-out succulent soil, don't water for a week, then mist them rarely. Most of them will grow roots on their own, it's a succulent after all. And the plant itself recovers pretty quickly once conditions get back to normal!