Hello again, Jason.
Unless the type of work or wages are substantially changing, an employee would not typically be eligible for unemployment benefits if they refuse the modified terms.
A rule of thumb that is usually used is a 20% or more reduction in wages or hours that may constitute good cause to reject the new offer and still collect unemployment benefits.
If there is some term of the employer's new "offer" that does substantially change the terms of your employment, please let me know and I would be happy to address that.
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