Only if they sell the debt to a creditor (hospitals and doctors can’t garnish wages) sue you, win, and pursue the judgement. And then they can only take from your disposable income (after rent, food, other bills, etc.)
And you can wipe out all of it by filing bankruptcy.
I have seen nothing about this - and know folks that were sued by the hospitals. It has been some years, mind you.
Is it possible that they cannot garnish wages in your state? Where are you getting your information?