Moderator's note: This thread is somewhat out of sequence because in order to help the new member with his questions the posts were consolidated in one thread. The computer put the posts in chronological order so the actual first post of this thread was moved down to post #5. Sorry for the confusion.
The sway bar is connected using sway bar links which are held on by a nut and bolt. It probably came loose and fell off, it is probably not broken just needs a new nut and bolt. Given that this was at a dealership, have them tow it back at their expense. It is not recommended to drive unless you can connect the sway bar again.
Is the sway bar link disconnected or did the sway bar bracket (The one that holds the sway bar up) actually come loose/break?