Although federal officials have long recognized improper spending as a problem, it is not the main reason for the program’s dire financial outlook

The involvement of Antonio Gracias, an investor who has known Elon Musk for two decades, suggests that Mr. Musk has made overhauling the Social Security Administration a priority.

Elon Musk pushed debunked theories about Social Security on Monday while describing federal benefit programs as rife with fraud, suggesting they will be a primary target in his crusade to reduce government spending.