I've seen that clause before when I worked for a brief time at a SNF. They made it clear, if you didn't give a 4 week (!) notice they docked you back to minimum wage for your last check. You had to sign paperwork that you read and understood the Policies and Procedures when you hired on so they really had you boxed in.
I got around that by going to contingent then just didn't pickup up any shifts.
Like the other posters have said, forget the wages you lost. I'd be far more concerned about the narcotics allegation. That could bite you in the behind and jeopardize your license.