Assuming you are emancipated, or can otherwise lawfully establish your own residence at the age of 16, you should be free to do so - that is, establish your own independent residence.

As emancipation means that you are independent of your parents, if you are emancipated they probably won't have any duty to support you. As emancipation usually requires that the minor establish financial independence, and financially independent people don't ordinarily need government assistance, you probably can't count on government aid either.

Please do inquire with a local lawyer, and report back to us with any definitive information you obtain. That should be helpful to anybody else who comes along, who has a similar situation.