You're right; it's illegal. Call a local tenant's attorney.
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That LL has got some nerve. Not sure what you'll be able to get back since you agreed to his request--but next time your shift comes up--consider being a no show.
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Depending on what is in your lease, requiring you to clean a common area that you don't have sole access and control does violate the law. A provision for "fining" you also likely violates the consumer protection statute. Talk to a lawyer... What is happening doesn't sound lawful.
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