Before there were rudders there were steering boards, usually attached to the right side of the boat which is why we still call it the "star board" side. And because you could smash the steering board against a jetty, they tied the other side of the port to the jetty when they were in port. So the left side became the port side of the boat.
Steering boards still work, anything that spoils the hydrodynamics of the boat and makes it turn one way or the other can steer it. On a nicely balanced boat, you can also steer by trimming the sails and the rudder should be dead center, pretty much. So...aside from the new designs that have next to no stability without a rudder? Losing it should fall into the category of "damned inconvenience" not "emergency".
Having a full keel, so the boat tracks in straight line, will of course help if you are trying to make do without a rudder. That's one reason traditional cruisers may favor a full keel, too.