No, there are no specific tax breaks for being unemployed.
Unemployment is taxable income on your federal tax return. And there are some states that tax unemployment--so whether your state taxes it depends on the tax laws in your state. You will receive a 1099G from the state which must be entered on your tax return. Sometimes they mail it to you; more often you have to go to the state's unemployment website to get your 1099G. CA does not tax unemployment.
Any other income you receive during the tax year must also be entered on your tax return, whether that income is on a W-2 or some other tax document.
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