See other failures under 000.html.
Three axle failures, one Shimano cassette hub, one rider. From http://zerodish.wordpress.com/2010/08/14/broken-axles as of 2014/08.
No reports of rider injuries. Service history unknown. No notes on how the failures were discovered.
Historically, freewheel hubs broke most often where the axle was badly overhung (cantilevered) under the freewheel. Failures are due to a combination of high stress, frequent load cycles (e.g., once per pedal stroke), and the axle threads which act as stress risers. More on the problem and some historical solutions at FAIL-165.
The failures shown above are similar but as noted at the original page, the cassette mechanism used here places the right bearing closer to the dropout than the left. Although the axle loads at the left bearing are less than on freewheel hub right bearings, the loads are still non-trivial.
Further, this wheel in particular has been shifted right slightly to reduce dish, slightly increasing the overhang/leverage on the left bearing. The shift is small and may have slightly accelerated failures, but it seems likely that similar failures would have occurred even without re-dishing.
The page where these axles appear says (as of 2014/08) "One partial solution is to use a solid axle these are about 30 percent stronger." For the failures shown here, a solid axle is about the same strength and might even be weaker than a hollow "quick-release" axle:
Bending loads are mostly carried by the "skin" of the axle. In bending, one side goes in tension and the other side in compression. Metal near the middle of the axle carries almost none of the load.
Solid axles are often (not always) built for low-cost bicycles and are of weaker materials than hollow axles built for high-cost bicycles. This has nothing directly to do with "hollow" or "solid" — there are also cheaply-made hollow axles — but it may take significant effor to find a solid axle of good materials.
If the quick release skewer is very tight, it slightly pre-loads the axle. With bending load, the "tension" side is initially in compression and must first reduce compression to zero before it can go in to tension. A solid axle never has such pre-load.
See also FAIL-.html.