There's two issues.
1 - Backdating a reduction in pay is illegal. Deducting the arrears from your pay without your consent is illegal. So, obviously, it would be a bad idea to sign the consent. Just make sure you talk to somebody at your state's wage and hour regulatory agency to confirm what I've written.
2 - Is the reduction in pay considered constructive termination for UI benefits or does it give you good cause to quit and collect benefits. I don't think so. I think that, as long as you are being paid minimum wage you would not be eligible for UI if you quit due to the reduction.
Here's the UI website:
And here's the UI statutes: