Can a 16-year-old be Emancipated if they currently have no income or place to live due to parents without parental consent?

Doubtful. If the state even has an emancipation statute, one of the key items that must be shown is that the minor is able to take care of themselves. Without income and a place to live that is pretty hard to do. Check the statutes for your state to see if there is an emancipation law, and what the requirements are if one exists.