I need help - payments ending

SSI is meant for low-income folks who are :

• aged (age 65 or older) or
• blind or
• disabled

So unless your children are blind or disabled I'm not sure how they can receive SSI benefits.

http://www.ssa.gov/ssi/text-eligibility-ussi.htm

As far as "normal" Social Security benefits, children can receive Social Security benefits if they 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.

So if the father is retired, disabled, or deceased, the children can receive their "own" benefits in this case.

http://www.ssa.gov/pubs/10085.html#a0=0

I assume DCF means "Department of Children and Families" , although I'm not sure of the state. We're not experts in this area, but I understand there can be exceptions to the "lifetime limit" on benefits which you may want to explore.

Bless you.