I took the car to the shop last week and they said it needs a new intermediate steering shaft. What happens if this goes untreated for a long time? The car is a 2001 Chevy Cavalier.
It depends why it's making the noise and what exactly is wrong with the shaft.
Having no power steering is superb ime, you can feel the road and control the car much more effectively.
But, the obvious answer is that the shaft is part of a mechanism that makes the car change direction when the operator turns a wheel inside the vehicle. If that functionality ceases to work when the car is in motion then it will tend to move in the direction it was heading until some force acts upon it, perhaps a panicing driver, or maybe a wall or a tree. Or maybe you'll stop the vehicle on the wrong side of the road because at the time it breaks you are overtaking someone. Then if you get out the car quickly enough, or the oncoming traffic stops in time, you'll have a story to tell us.
OTOH, I found turning up the radio was a good way of removing annoying noises from cars I've owned in the past, which continued for years with no other ill effects.
But you know that.