Obviously, parents don't need to use their child's social security number early in their lives so they may not realize that number has fallen into the wrong hands.
The Social Security office in Philadelphia says it's aware of this trend and to make sure your child's number isn't being used: run regular credit checks with the three credit reporting companies and check routinely with the Social Security Administration.
Social Security Links:
http://ssa-custhelp.ssa.gov/app/answers/detail/a_id/77
http://ssa-custhelp.ssa.gov/app/answers/detail/a_id/625
Getting a Free Credit Reporting From 3 Credit Reporting Companies:
https://www.annualcreditreport.com/cra/index.jsp