Being on unemployment has nothing to do with your eligibility to receive life insurance death benefits.
If you are an individual named as the beneficiary to a life insurance policy you would receive the death benefit, if the insured person died, subject to any exclusions.
For instance, you wouldn't be able to get the death benefit if you were responsible for killing the insured person.
But, otherwise, you should be able to receive the proceeds from the life insurance policy if you were named as the beneficiary on the life insurance policy