Vertical collaborative learning system also known as vertical federated learning (VFL) system has recently become prominent as a concept to process data distributed across many individual sources without the need to centralize it. Multiple participants collaboratively train models based on their local data in a privacy-preserving manner. To date, VFL has become a de facto solution to securely learn a model among organizations, allowing knowledge to be shared without compromising privacy of any individual organizations. Despite the prosperous development of VFL systems, we find that certain inputs of a participant, named adversarial dominating inputs (ADIs), can dominate the joint inference towards the direction of the adversary's will and force other (victim) participants to make negligible contributions, losing rewards that are usually offered regarding the importance of their contributions in collaborative learning scenarios. We conduct a systematic study on ADIs by first proving their existence in typical VFL systems. We then propose gradient-based methods to synthesize ADIs of various formats and exploit common VFL systems. We further launch greybox fuzz testing, guided by the resiliency score of "victim" participants, to perturb adversary-controlled inputs and systematically explore the VFL attack surface in a privacy-preserving manner. We conduct an in-depth study on the influence of critical parameters and settings in synthesizing ADIs. Our study reveals new VFL attack opportunities, promoting the identification of unknown threats before breaches and building more secure VFL systems.