The Compassionate Allowances program is a significant support system for people struggling with terminal illnesses. Designed to expedite the evaluation process for SSDI claims, this program is particularly helpful for those with severe medical conditions, including certain terminal illnesses. Conditions listed under this program go through a quicker review, ensuring faster access to benefits without enduring long waiting periods. Social Security Disability Lawyer. Proving terminal illness is the key to expediting SSDI claims. Evidence for terminal conditions needs thorough medical documentation showing the seriousness and prognosis of the illness.