Final answer:
When a family agrees to seek help on a voluntary basis without court involvement, it is known as Voluntary services. This approach allows families to receive assistance in a collaborative and non-coercive manner.
Step-by-step explanation:
When collaborating with a family that agrees to accept assistance voluntarily, and without the need to involve a court, this kind of assistance is known as Voluntary services. This is in contrast to involuntary intervention, which occurs without the family's consent, or court-ordered treatment, which is mandated by the legal system. Legal arbitration differs from this because it typically involves an impartial third party making a decision for the parties involved in a dispute, which is not the case here where the family has agreed to services without any such mandate or third party decision-maker.