No, and in fact she might get her boyfriend in major trouble, too. A minor cannot enter into contracts, cannot make decisions that require emancipation and adulthood, and so much more......
More information is necessary to expound on this......
You probably know she has a lot more going on in her story at home. Check with a lawyer in your locale to discuss more of the details. Get her the help needed! Do not wait!
Good luck to you.
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"Can a minor run away at age 16 and not get into trouble?" If her parents do not care what she does and she causes no trouble to bring her to the attention of anyone else, she can.
Presumably, her parents would care and may be able to cause the police to investigate the boyfriend, especially if he is much older. While the age of sexual consent in WA is generally 16, the boyfriend likely can be charged with other crimes since the girl is a minor.
If the girl needs to go see a doctor or other professionals, those people may start wondering where the girl's parents are and file reports with the police, CPS, or other government offices.
Incidentally, running away from home, moving in with a boyfriend and expecting to "be fully supported by him" likely is not a good way to live for most people.
If you are the girl, please carefully consider your options. Talk with your school counselor, other professionals, or other adults whom you trust for help.