I've had CFL's that were failing start to flicker, and thus overheat so that the plastic base starts to get scorched or even slightly melted. But they always quit completely before it got hot enough to cause any serious problem.
The only real safety concern I know of is that the bulbs contain some mercury, so if one gets broken that mercury will be exposed on the broken pieces, and someone cleaning it up could get it on their body. Thus the recommendation that you use cardboard to scrape up the pieces, and discard that along with the broken pieces -- don't use a broom or vacuum to clean up a broken cfl (or fluorescent tube, either).
However, the amount of mercury is really tiny -- about 1/20th of that in a thermometer -- and I think some people are rather hysterical about this.