Filing for Social Security disability while receiving unemployment benefits is very difficult. The problem is that you are saying two different things to collect each type of benefit. When you are on unemployment, you are stating that you are ready and willing to perform work, but that you simply cannot find a job that fits your skills. When you are applying for Social Security disability benefits, you are stating that you cannot work for a period of at least twelve (12) months due to physical or mental limitations. In most cases, the safest practice is to not be on unemployment while applying for social security disability benefits. Administrative Law Judges will often look with disfavor on applicants who are on unemployment. Some will even outright deny claims on that basis alone.
However, if you are over 50, you may be able to collect disability benefits while on unemployment. The reason for this exception, is because after an applicant reaches 50, they are eligible to collect disability benefits under the medical-vocational allowance grid. This grid allows for older workers to qualify for disability benefits if they have limited education and limited residual skills. Therefore, in this limited circumstance it is still possible for someone to collect disability benefits while on unemployment. But it is still a risk for even an individual over 50 to try to do so.