It is not possible to seek unemployment benefits while pursuing a disability claim, even if a worker was laid off for reasons unrelated to their disability. The problem is that unemployment benefits are only awarded to people who are actively seeking employment. If they are not pursuing full-time employment, they are not entitled to unemployment compensation.
Since applicants must be unable to maintain gainful employment to qualify for SSD, seeking full-time employment would indicate to the SSA that they are not too disabled to work. Applicants are typically entitled to pursue one type of benefit or the other, not both.