Were these bearings defective? A couple of days ago my girlfriend's bicycle broke. The rear wheel was stuck. Tonight I had finally some spare time to have a look. The bearings had failed, so much so that the wheel must have spun for some time piecewise with the axle.

As a consequence, if you are picturing this right, the left nuts had tighten as that very hot place, whereas the nuts and cup on the drive side were completely loose (the axle had screwed itself to the left).

I don't know what caused this. I had replaced the bearings in the past, something I've done many many times with no problems. What I'm asking here is whether this level of damage is normal or the bearings are cheap.
I mean: the rightmost bearing in the picture can be separated into a smaller (about 3/16) inner ball and an outer 1/4" shell!

This is the first time I used bearings from ebay, and would like to have your opinions.
I've also never seen a bearing ball fail like that.  In Jahaziel's answer to this question:

When do bearings need to be replaced? 

he notes that in Honduras where he lives they sometimes could only get cheap Chinese bearings that "used to 'peel off' like an onion".  Perhaps you got some of those?  See also the response of "Mike" in this thread [1], who had a similar (albeit worse) experience with cheap bearings.  

Good properly tightened bearings should last for many thousands of miles/kms, and usually races tend to show the damage more clearly before the balls do.  I've never actually over-tightened a hub and tried to ride on it to see how it fails when it seizes (and I'm not saying you did that, but it's the only other explanation I can think of other than cheap bearings), but based on both the SKF paper linked above and this paper [2] and this analysis [3] it seems like ball bearings delaminating or fragmenting is not the most common failure mode, because none of them discuss it.  Particularly in [3] you can see that the balls in seized bearings  polished off a contact patch against the race rather than disintegrating.

[1] http://www.bikeforums.net/archive/index.php/t-23340.html

[2] http://www.elongo.com/pdfs/BearingFailures990519.pdf 

[3] http://met-tech.com/failure-analysis-of-ball-bearings.html