Benefits for children of disabled parents

Yes, this may be possible.

Your child can get benefits if he or she is your biological child, adopted child or dependent stepchild. (In some cases, your child also could be eligible for benefits on his or her grandparents’ earnings.)

To get benefits, a child must have:

* A parent(s) who is disabled or retired and entitled to Social Security benefits; or
* A parent who died after having worked long enough in a job where he or she paid Social Security taxes.

See here for details :
http://www.ssa.gov/pubs/10085.html