Receiving unemployment benefits can be a problem if you have a claim for Social Security disability insurance (SSDI) or Supplemental Security Income (SSI) because you are making two inconsistent statements:
1) To get unemployment benefits, you are claiming that you are able to work, but cannot find a job.
2) To get Social Security disability benefits, you are claiming that you cannot perform any type of work at a substantial gainful activity level (generally full time work).
It is possible to get both unemployment and Social Security disability benefits because of the different standard of work required under unemployment vs Social Security disability.
BUT, trying to get both may turn off Social Security and hurt one's chances of winning a case.