I got bored at lunch, so decided to take up my request to find what has happened when a lower control arm failed. Stories about cars in the links below. I skipped the common off-road failures in SUV's and trucks.

Broken Lower Control Arm - Appearance - Red Pepper Racing
Lower Control Arm Fails-BOOM-Rust. Need tips on repair. - MBWorld.org Forums
Broken lower control arm on my M3
1996 E300D front control arm collapse | Mercedes-Benz Club of America
Ever had a lower control arm break? - Chevelle Tech

In my "get 'er home" trip, I was only worried about keeping the LCA "pivot cup" in position, since if it moved outward again the right front wheel would toe-out. The chain (2500 lb break strength) pretty-well assured it could not rotate outward. The cup was still solidly attached to the K-frame (other than for tilting). The LCA in our 300D's appears to be solid forged steel, not the wimpy welded sheet-metal one sees in many cars.

For some cars, it seems that LCA breakage while driving is not uncommon (many "mine broke too" comments). Sounds like mostly metal fatigue, since often happened on fairly smooth pavement. In all cases, the suspension and front tire simply dragged on the ground until the car stopped. They didn't drift into another lane or roll over. Many scarier things one could worry about while driving. Perhaps a little gunk or rubber hose bit plugs the spool valve in your power steering gear, making it decide to steer hard left. Could you over-power it? Always belt up.