In the state of MA, can a 16 year old move out without parental consent.

Probably not. Mass. does not have a law or guidelines for setting an age, or situation, where a child is considered emancipated. Although the law recognizes 18 as the age of majority. So, if you wished to get married at 16, a parent might block it. You may request the court in the local Probate and Family Court to declare you are emancipated, if the court feels that such a declaration is in your best interests. The court will look at a lot of different criteria for this. Getting a lawyer may prove helpful, or wait until you are 18.

This is a Juvenile Law, more than a Family Law, issue, so I changed the category. Moving to a friend's house before you turn 18 could result in your parents filing a Child Requesting Assistance (CRA, formerly known as CHINS) case against you. See my article linked below. You might also subject your friend's parents to charges of contributing to the delinquency of a minor. See Mass. General Laws chapter 119, section 63; also linked below. If there are problems at home, such as abuse or neglect, your friend's parents may want to consider filing a guardianship petition in order to get court-sanctioned custody of you. They will likely need to hire a Guardianship attorney since, if your parents contest the petition, your friend's parents will have to introduce evidence to convince the judge that your parents are currently unfit and that it is in your best interests to give custody to the petitioners. I have linked the Massachusetts Trial Court Law Libraries' resource page on "Massachusetts Law about Guardianship and Conservatorship" below. And since Atty. LaPre mentioned emancipation, I have also linked below the Massachusetts Trial Court Law Libraries' resource page on "Massachusetts Law about Emancipation of Minors".