Historically, the general rule was that a parent is not responsible for the acts of a child. However, the Oregon legislature has largely changed this rule by enacting several laws that allow limited liability of a parent for the acts of a child. Accordingly, the rule in Oregon is that the parent or guardian of a child under the age of 18 can be held financially responsible for acts committed by the child that injure or damage another person, or another person's property.
Liability generally comes from the acts of the child — and/or the negligence of the parent or guardian as it relates to the acts of the child. For example, a parent or guardian can be held liable for negligently allowing their minor child to operate a vehicle if that act resulted in injury to another and the parent or guardian knew or should have known the child was not a competent driver.
In Oregon a legal custodial parent of a minor child can be held civilly liable for the shoplifting of a minor child for the value of the merchandise shoplifted up to $500. At the time of this writing, the parents can also be held liable for a penalty to the merchandise owner of no less than $100 and no more than $250, in addition to the value of the merchandise shoplifted.
A parent or guardian is not responsible for a child's act if the child has been legally emancipated or is married. Emancipation is a legal proceeding in which the juvenile court has declared that a minor over 16 can legally live on his or her own and enjoy many adult rights and responsibilities. (Your child cannot be "emancipated" without using this proceeding.)
If parents are divorced, the parent who has custody of the child is the one financially responsible for any damages the child causes. Foster parents do not have financial or legal responsibility for the intentional, destructive acts of the foster children in their care, and may make their own claim to DHS for damages to them done by the foster children in their care.