Can Parents Emancipate Their 17 Year Old

My daughter has a friend. Her parents told her to quit school and work and they withdrew her from school. She didn't want to do this and wants to finish her senior year. I told her she can stay with us. I told the mother also. She came today and said that her parents will only let her stay with me if she is emancipated. Can they force this on her? Is it in her best interest? They have already listed me as the one the school will talk to(she has already re-enrolled herself). They told her that they will start the process but it sounds like she has to pursue this course, is that accurate. She is 17, a senior, has a part time job, has good grades, but there is really little chance that she can support herself as she goes to school, and what about insurance?
We are in Washington state.

Her parents are responsible for her until she turns 18, whether they want to be or not.

They cannot kick her out, "have her emancipated" or pull her out of school. Additionally, if she is not working full time and cannot completely support herself, no judge will grant her emancipation petition, regardless of what her parents want.