I could see one of two scenarios: 1) the twins naturally died and she concealed their deaths so she could keep collecting benefits from the government from them.
2) the twins died of neglect, some accident, or foul play and she hid their deaths because she didn't want to end up in trouble.
I don't see how they could still be alive. If she gave them away, why not tell where they are? If the twins died naturally I don't see why she she hasn't said what actually happened at this point because she's no longer able to collect the twins' benefits. As a result, I feel scenario 2 if very likely as to what happened to those poor children.