Are there sliding shower-stall doors that are made of some kind of UNBREAKABLE glass or plastic?”
Most, if not all, shower doors are made of tempered glass, which resists shattering, for precisely the reason you mention. Here is a model: http://www.plumbersurplus.com/Prod/DreamLine-SHDR-1060726-00-Infinity-Sliding-Shower-Door-White/77485/Cat/1190?utm_medium=referral&utm_source=googlebase&cvsfa=63&cvsfe=2&cvsfp=77485 However, the door you have now is probably made of tempered glass already.