There exist several hand exoskeletons systems that provide assistive force to the user for strength enhancement or rehabilitation. However, the lack of stability analyses for such systems has made it difficult to ensure that these systems can apply assistance forces corresponding to the user's intended motion. In this study, a tendon-driven soft hand exoskeleton was developed to provide assistive grip force, and the qualitative stability condition of the system was investigated during system operation. The proposed exoskeleton assisted the middle finger, index finger, and thumb, based on the fingertip force estimated using a previously developed fingertip force sensor. This system applies a flexion force for the middle and index fingers, as well as flexion and abduction forces for the thumb. Because the stability of the system is important during the operation of the system, we qualitatively analyzed the stability condition of the system based on the modified form of the generalized unstructured model comprising the user's finger, exoskeleton, and external environment. An experimental verification of the stability criterion was performed to determine the approximate range of the stably applicable assistance gain. This study is the first to quantify the stability of fingertip sensor-based assistive power being applied to the hand.