This is like a reverse test to determine swelling potential of soils. There is an ASTM Standard Test method for this evaluation. Refer to Volume 4.08 or 4.09. Also, see the Bureau of Reclamation book Design of Small Dams. It has a chart relating the ratio of insitu dry density to the Standard Proctor dry density and the difference between optimum water content to insitu water content to collapsibility.
Collapsible soils are often mud flow alluvial fan or windblown silty clays.
They are characterized by a visible porosity, a low dry density and low natural water contentt. In addition to what the others have said, you can recognize collapsible soils from their low density, their geologic deposition, and using lab compression tests. If the water content of the soil at saturation exceeds the liquid limit, the soil will collapse if it gets saturated. Design should include sloping the ground surface away from the structure, using foundation drains, extending downspouts at least 10 feet away from foundations, making sure water cannot pond close to structure, being aware of automatic sprinkler systems, etc. On big projects, the ground can be made to collapse prior to construction by the addition of ponded water, followed by preloading to take out additional settlement.