From a recent report by Social Security's Office of Inspector General (OIG):
... Since SSI is a program of last resort, SSA requires that individuals apply for all other benefits for which they are potentially eligible, including VA benefits. In a January 2010 report,we estimated SSA paid approximately $1.3 billion to 21,520 SSI recipients who appeared to meet VA’s requirements for benefits.To conduct our current review, we identified 1,327 SSI recipients (from 1 of 20 Social Security number segments) who appeared to meet VA’s requirements for benefits. We randomly selected 50 cases for detailed analysis. ...
SSA improved its process of identifying SSI recipients potentially eligible for VA benefits. We estimated approximately 7,960 SSI recipients appeared to meet VA’s requirements, a nd SSA had not documented VA’s final determination for benefits or continued SSI payments even though recipients had not filed for VA benefits. This is 63 percent fewer than the estimated 21,520 SSI recipients in our prior report. ...