My oldest threatened to run away once. I packed her bag and put it and her on the front porch and closed and locked the door. She was out there a total of about 2 minutes before she was yelling she was sorry and please let her come back home.
Then another time she threatened to call DFCS (child protective services) because I grounded her. I told her to go ahead, but to keep in mind it would take them about 20 - 30 minutes to get here and God help her while they were on their way. I also told her I didn't have a problem with going to jail. Jail would be a VACATION for me. I wouldn't have to worry about who had to be where at what time and what they were going to where, etc. I wouldn't have to worry about what was going to be for dinner. She straightened herself up real quick and has never threatened to call again.