There is no specific SSA rule that states that you cannot apply for Social Security Disability while on unemployment. However, as a practical matter, it may be difficult to receive benefits from both. This is because most state unemployment regulations require one to attest that they are capable of working and looking for employment. This is opposite to SSDI, where you must be unable to work to qualify. This can put an applicant for SSDI in a difficult position with an Administrative Law Judge (ALJ) that questions an applicant that has represented to a state agency they can work but tells the SSA and the ALJ they cannot.
My experience is that some ALJs will not find someone disabled during a period of time they collect unemployment, while unemployment has no impact with other ALJs decisions. If one chooses to file for disability while on unemployment, you should consult with an experienced Social Security Disability attorney to discuss their specific situation. Depending on your age and specific limitations, there may be some acceptable explanations, such as applying for part-time work, applying for work with request for specific disability related accommodations or you are old enough for certain "grid" rules to apply to your situation.
