I'm Lucy, and I'd be happy to answer your questions today. I'm sorry to hear about your situation.
Because employment is at will, your employer unfortunately can cut your pay unless you have a contract stating that you can only be terminated for cause. Essentially, he's letting you go and offering to rehire you at the new, lower salary, and this is allowed. The minimum wage in Massachusetts is $10/hour, so he cannot go below that, but it's otherwise allowed. You have a right as an employee to reject the pay cut and seek other employment.
When a person is fired due to attendance, that's legally considered job abandonment, and you unfortunately would not be eligible for unemployment. However, if your manager cuts your pay substantially, that could be considered good cause for quitting.
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