Yes, and it happens quite often. Remember, for Social Security Disability (SSD), you must also meet the insured status. Many people whose insured status has expired because they haven’t worked recently can get Supplemental Security Income (SSI) if they can prove a recent disability. You can also get disability and not get Supplemental Security Income (SSI). Frequently a person’s Social Security Disability (SSD) monthly benefit is too high to be eligible for additional Supplemental Security Income (SSI) benefits (remember it is called “Supplemental Security Income”). If you are not impoverished, you are never eligible for Supplemental Security Income (SSI), even if you are disabled. Many people can receive both. The definition of disability is the same for Supplemental Security Income (SSI) and for Social Security Disability (SSD) and the appeals process is the same for both.