Is it permissible not to inform the U.S. government of a man's death to preserve his orphaned children's income, and is it permissible to forge official documents to prove he is still alive for the same reason?

It is not permissible to deceive the state and conceal the father's death to continue receiving his salary. Rather, the authorities must be informed of his death, because concealing the matter is considered devouring wealth unjustly. The fact that the orphans have no provider does not make deception permissible. If there is no one to support them, their sustenance becomes obligatory from the Muslim treasury (Bayt al-Mal), if one exists. Otherwise, it falls upon the closest Muslim relatives, then the next closest.