You tell the truth regardless of the consequences... otherwise you are potentiall criminally liable..
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collecting ua benefits is a factor when trying to get ssd. it is ok to indicate you are available to try to work, but you will need to explain it at a ssd hearing. it should be noted the statutes are not consistant. for example, a person may think they can do a sit down job and tell that to the unemployment agency, even though they are over 50 and have never done a sit down job. this could get them ua benefits and at the same time they might be disabled under ssd rules that say if you do not have skills that transfer to sit down work you are disabled in many cases.