Emancipation is not and never was intended to be a means to allow a minor to leave home, no matter how bad their situation is. It was and is intended to be a means of providing legal protections to a minor who, for reasons outside their control, found themselves living on their own.
I don't know off the top of my head what TN's rules for emancipation are, even if you qualified (which you don't) but if you are not capable of paying EVERY SINGLE CENT of what it costs to support you (that means rent, food, utilities, clothing, transportation, medical care, insurance, staples, school fees and supplies, etc. - all paid, or at least budgeted, 100% by YOU, without the help of friends, relatives, or the state) then no judge will emancipate you no matter how bad your situation is.
In no state can a 16 year old legally leave home without parental permission, particularly not to leave the state. If you did so, when (that's when, not if) your parents and/or law enforcement caught up with you, the people you were staying with could end up in jail for allowing you to stay there against your parents' wishes.
If you are truly being abused, then call the Child Protective Services.