Generally offshore trusts are similar in nature and effect to their onshore counterparts; they involve a settlor transferring (or 'settling') assets (the 'trust property') on the trustees to manage for the benefit of a person, class or persons (the ' beneficiaries ') or, occasionally, an abstract purpose.enerally offshore trusts are similar in nature and effect to their onshore counterparts; they involve a settlor transferring (or 'settling') assets (the 'trust property') on the trustees to manage for the benefit of a person, class or persons (the ' beneficiaries ') or, occasionally, an abstract purpose.