Do you have examples ? I have never heard European people being sued for quitting either. The opposite of at-will employment is not that you can't quit. Just that employers can't suddenly fire you without repercussions.
The more common way to do this these days is to feign an illness like stress and get signed off work, paid, by the doctor, then quit later.
Paid by the doctor? I think sick pay comes from the employer initially and later statutory sick pay(state).
If you have three months notice period in your contract, your employer could sue for loss of income if you don't honour that notice period.
It usually doesn't happen that way, because it is a waste of everyone's time and money. But, if some employer feels the need to set an example the option is there.
Most people make an extra effort to end on a positive note, both with colleagues and managers. Of course, effectively off-boarding yourself means having progressively less and less to do as time goes by... So in that sense you sort of quiet quit.
Its not very likely and hard to prove damages by the employer, but possible.
Nothing really stopping you from simply half-assing your job during your notice period, though.