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Most people cannot collect both unemployment and disability benefits at the same time. Although the SSA claims receiving unemployment does not prevent you from also receiving disability benefits, there are reasons why receiving unemployment while applying for disability could work against you.
When you receive unemployment, you are stating that you are ready and able to return to work, and that you are actively searching for a job. When you apply for disability, you are stating that you have a physical or mental condition that makes it impossible for you to work for at least a year. These two statements conflict with each other.
The Administrative Law Judge who reviews your case could consider this conflict grounds for denial.