A veteran can receive Social Security Disability Insurance (SSDI) alongside total disability based on individual unemployability (TDIU) benefits. The Social Security Administration (SSA) and the VA work independently of one another, meaning that a decision from one agency will not impact the other.
Also, the amount veterans receive in SSDI benefits will not be reduced because of their VA benefits, so it can be beneficial to apply for both. The two benefit programs have different eligibility requirements which means some veterans will qualify for one or the other and some will qualify for both.