What Is The Name And How To Repair? Help Needed

I was coming back from a trip to the local mountains on the Ortega highway between San Juan Capistrano and Lake Elsinore. I had noticed a vibration on decelleration, decided I'd check it out when I got home. Well, the rear driveshaft comes loose, flailing against the tub floor. Made quite a racket. As above, I removed the still-attached end and drove home to Orange on the front axle. I suspect many Jeepers have had an experience like this.