We propose a dual-cable method of stabilizing the thumb in the context of a hand orthosis designed for individuals with upper extremity hemiparesis after stroke. This cable network adds opposition/reposition capabilities to the thumb, and increases the likelihood of forming a hand pose that can successfully manipulate objects. In addition to a passive-thumb version (where both cables are of fixed length), our approach also allows for a single-actuator active-thumb version (where the extension cable is actuated while the abductor remains passive), which allows a range of motion intended to facilitate creating and maintaining grasps. We performed experiments with five chronic stroke survivors consisting of unimanual resistive-pull tasks and bimanual twisting tasks with simulated real-world objects; these explored the effects of thumb assistance on grasp stability and functional range of motion. Our results show that both active- and passive-thumb versions achieved similar performance in terms of improving grasp force generation over a no-device baseline, but active thumb stabilization enabled users to maintain grasps for longer durations.