I just wanted to add that my Dh and I were in a similar situation 9 years ago. Our 15 year old Dd decided that she wanted to live with a chap twice her age and refused to come home one night.
We rang the police who, I have to say, were fantastic to us and they sussed out where this chap lived and went round straightaway. Our Dd refused to come home and got very abusive to them so they put handcuffs on her and took her to the local police station.
The officer rang to tell us all of this and after asking us if we wanted her home (he said if she was his he would change his locks and never have her back) and they then brought her home.
We had a long talk, one of many, and she agreed to stay at home until she turned 16. Not to please us, I hasten to add, but so that the man would not get into trouble with the police. She was underage after all.
To cut a long story (sorry) short she did leave home when she was 16 and moved in with this man. 9 years on they are as happy now as they were then and our Dd is so close to us now.
We actually laugh hysterically now at what we call handcuffs day. There is light at the end of the tunnel sometimes and I would say keep the lines of communication open if at all possible. Good luck.