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You may apply but your unemployment benefits can be reduced or eliminated by your social security income. It depends on how much unemployment and your social security benefits.
According to MA guide to benefits, social security benefits are not considered a reportable income. Which means, in Massachusetts you can collect SS benefits and full unemployment benefits at the same time.
http://www.mass.gov/lwd/docs/dua/p2594-508.pdf - scroll down to page 18